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hreflang="gl" data-title="Relación área superficial-volume" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rasio_luas_permukaan_terhadap_volume" title="Rasio luas permukaan terhadap volume – Indonesian" lang="id" hreflang="id" data-title="Rasio luas permukaan terhadap volume" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Jumlah_luas_permukaan_per_isi_padu" title="Jumlah luas permukaan per isi padu – Malay" lang="ms" hreflang="ms" data-title="Jumlah luas permukaan per isi padu" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa 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src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Comparison_of_surface_area_vs_volume_of_shapes.svg/300px-Comparison_of_surface_area_vs_volume_of_shapes.svg.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Comparison_of_surface_area_vs_volume_of_shapes.svg/450px-Comparison_of_surface_area_vs_volume_of_shapes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Comparison_of_surface_area_vs_volume_of_shapes.svg/600px-Comparison_of_surface_area_vs_volume_of_shapes.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Graphs of surface area, <i>A</i> against volume, <i>V</i> of the Platonic solids and a sphere, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume. Their intercepts with the dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times.</figcaption></figure> <p>The <b>surface-area-to-volume ratio</b> or <b>surface-to-volume ratio</b> (denoted as <b>SA:V</b>, <b>SA/V</b>, or <b>sa/vol</b>) is the <a href="/wiki/Ratio" title="Ratio">ratio</a> between <a href="/wiki/Surface_area" title="Surface area">surface area</a> and <a href="/wiki/Volume" title="Volume">volume</a> of an object or collection of objects. </p><p>SA:V is an important concept in science and engineering. It is used to explain the relation between structure and function in processes occurring through the surface <em>and</em> the volume. Good examples for such processes are processes governed by the <a href="/wiki/Heat_equation" title="Heat equation">heat equation</a>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> that is, <a href="/wiki/Diffusion" title="Diffusion">diffusion</a> and <a href="/wiki/Heat_transfer" title="Heat transfer">heat transfer</a> by <a href="/wiki/Thermal_conduction" title="Thermal conduction">thermal conduction</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> SA:V is used to explain the diffusion of small molecules, like <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> and <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a> between air, blood and cells,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Water" title="Water">water</a> loss by animals,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> bacterial morphogenesis,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> organism's <a href="/wiki/Thermoregulation" title="Thermoregulation">thermoregulation</a>,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> design of artificial bone tissue,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> artificial lungs <sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and many more biological and biotechnological structures. For more examples see Glazier.<sup id="cite_ref-:0_9-0" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The relation between SA:V and diffusion or heat conduction rate is explained from flux and surface perspective, focusing on the surface of a body as the place where diffusion, or heat conduction, takes place, i.e., the larger the SA:V there is more surface area per unit volume through which material can diffuse, therefore, the diffusion or heat conduction, will be faster. Similar explanation appears in the literature: "Small size implies a large ratio of surface area to volume, thereby helping to maximize the uptake of nutrients across the plasma membrane",<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and elsewhere.<sup id="cite_ref-:0_9-1" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>For a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is a <a href="/wiki/N-ball" class="mw-redirect" title="N-ball">ball</a>, a consequence of the <a href="/wiki/Isoperimetric_inequality#Isoperimetric_inequality_in_higher_dimensions" title="Isoperimetric inequality">isoperimetric inequality in 3 dimensions</a>. By contrast, objects with acute-angled spikes will have very large surface area for a given volume. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="For_solid_spheres">For solid spheres</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=1" title="Edit section: For solid spheres"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:SAV_n3.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/SAV_n3.png/220px-SAV_n3.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/SAV_n3.png/330px-SAV_n3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/SAV_n3.png/440px-SAV_n3.png 2x" data-file-width="1750" data-file-height="1313" /></a><figcaption>Plot of the surface-area:volume ratio (SA:V) for a 3-dimensional ball, showing the ratio decline inversely as the radius of the ball increases.</figcaption></figure> <p>A <i><a href="/wiki/Solid_sphere" class="mw-redirect" title="Solid sphere">solid sphere</a></i> or <a href="/wiki/Ball_(mathematics)" title="Ball (mathematics)"><i>ball</i></a> is a <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">three-dimensional</a> object, being the <a href="/wiki/Solid_figure" class="mw-redirect" title="Solid figure">solid figure</a> bounded by a <a href="/wiki/Sphere" title="Sphere">sphere</a>. (In geometry, the term <i>sphere</i> properly refers only to the surface, so a sphere thus lacks <a href="/wiki/Volume" title="Volume">volume</a> in this context.) </p><p>For an ordinary three-dimensional ball, the SA:V can be calculated using the standard equations for the surface and volume, which are, respectively, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SA=4\pi {r^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SA=4\pi {r^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/660887c08166696cc4672e79d39c861d04aa8f57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.938ex; height:2.676ex;" alt="{\displaystyle SA=4\pi {r^{2}}}" /></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V=(4/3)\pi {r^{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> <mo stretchy="false">)</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=(4/3)\pi {r^{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a83d82e4e2a72b3596604abc7ee1931c1b1a21e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.617ex; height:3.176ex;" alt="{\displaystyle V=(4/3)\pi {r^{3}}}" /></span>. For the unit case in which <i>r</i> = 1 the SA:V is thus 3. For the general case, SA:V equals 3/<i>r</i>, in an inverse relationship with the radius - if the radius is doubled, the SA:V halves (see figure). </p> <div class="mw-heading mw-heading3"><h3 id="For_n-dimensional_balls">For <i>n</i>-dimensional balls</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=2" title="Edit section: For n-dimensional balls"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Balls exist in any dimension and are generically called <i><a href="/wiki/N-ball" class="mw-redirect" title="N-ball"><i>n</i>-balls</a></i> or <i>hyperballs</i>, where <i>n</i> is the number of dimensions. The same reasoning can be generalized to n-balls using the general equations for volume and surface area, which are: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {r^{n}\pi ^{n/2}}{\Gamma (1+n/2)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {r^{n}\pi ^{n/2}}{\Gamma (1+n/2)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dd243cfa814eb0d4681cb0170379a81fbf4ca4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.706ex; height:6.509ex;" alt="{\displaystyle V={\frac {r^{n}\pi ^{n/2}}{\Gamma (1+n/2)}}}" /></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SA={\frac {nr^{n-1}\pi ^{n/2}}{\Gamma (1+{n/2})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SA={\frac {nr^{n-1}\pi ^{n/2}}{\Gamma (1+{n/2})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddda86d1e5ce8a467cfd666351719c2c0837e510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:18.161ex; height:6.509ex;" alt="{\displaystyle SA={\frac {nr^{n-1}\pi ^{n/2}}{\Gamma (1+{n/2})}}}" /></span></dd></dl> <p>So the ratio equals <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle SA/V=nr^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>V</mi> <mo>=</mo> <mi>n</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle SA/V=nr^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d82508b69348ca0ae1bb3c364a4a63aff4da0482" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.067ex; height:3.176ex;" alt="{\displaystyle SA/V=nr^{-1}}" /></span>. Thus, the same linear relationship between area and volume holds for any number of dimensions (see figure): doubling the radius always halves the ratio. </p> <div class="mw-heading mw-heading2"><h2 id="Dimension_and_units">Dimension and units</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=3" title="Edit section: Dimension and units"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The surface-area-to-volume ratio has <a href="/wiki/Physical_dimension" class="mw-redirect" title="Physical dimension">physical dimension</a> <a href="/wiki/Inverse_length" class="mw-redirect" title="Inverse length">inverse length</a> (L<sup>−1</sup>) and is therefore expressed in <a href="/wiki/Units_of_measurement" class="mw-redirect" title="Units of measurement">units</a> of inverse metre (m<sup>−1</sup>) or its <a href="/wiki/Unit_prefix" title="Unit prefix">prefixed</a> <a href="/wiki/Unit_multiple" class="mw-redirect" title="Unit multiple">unit multiples</a> and submultiples. As an example, a <a href="/wiki/Cube" title="Cube">cube</a> with sides of length 1 <a href="/wiki/Centimeter" class="mw-redirect" title="Centimeter">cm</a> will have a surface area of 6 cm<sup>2</sup> and a volume of 1 cm<sup>3</sup>. The surface to volume ratio for this cube is thus </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{SA:V}}={\frac {6~{\mbox{cm}}^{2}}{1~{\mbox{cm}}^{3}}}=6~{\mbox{cm}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>SA:V</mtext> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>cm</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>cm</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>6</mn> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>cm</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{SA:V}}={\frac {6~{\mbox{cm}}^{2}}{1~{\mbox{cm}}^{3}}}=6~{\mbox{cm}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35ef89aed7bf646eff0f13737bbf0e5e46b68f55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:25.268ex; height:6.009ex;" alt="{\displaystyle {\mbox{SA:V}}={\frac {6~{\mbox{cm}}^{2}}{1~{\mbox{cm}}^{3}}}=6~{\mbox{cm}}^{-1}}" /></span>.</dd></dl> <p>For a given shape, SA:V is inversely proportional to size. A cube 2 cm on a side has a ratio of 3 cm<sup>−1</sup>, half that of a cube 1 cm on a side. Conversely, preserving SA:V as size increases requires changing to a less <a href="/wiki/Compactness_measure_of_a_shape" class="mw-redirect" title="Compactness measure of a shape">compact</a> shape. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=4" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Physical_chemistry">Physical chemistry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=5" title="Edit section: Physical chemistry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Surface-area-to-volume_ratio" title="Special:EditPage/Surface-area-to-volume ratio">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2014</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Dust_explosion" title="Dust explosion">Dust explosion</a></div> <p>Materials with high <a href="/wiki/Surface_area" title="Surface area">surface area</a> to <a href="/wiki/Volume" title="Volume">volume</a> ratio (e.g. very small diameter, very <a href="/wiki/Porosity" title="Porosity">porous</a>, or otherwise not <a href="/wiki/Compactness_measure_of_a_shape" class="mw-redirect" title="Compactness measure of a shape">compact</a>) react at much faster rates than monolithic materials, because more surface is available to react. An example is grain dust: while grain is not typically flammable, <a href="/wiki/Great_Mill_Disaster" title="Great Mill Disaster">grain dust is explosive</a>. Finely ground salt dissolves much more quickly than coarse salt. </p><p>A high surface area to volume ratio provides a strong "driving force" to speed up thermodynamic processes that minimize <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free energy</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Biology">Biology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=6" title="Edit section: Biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Human_jejunum_microvilli_2_-_TEM.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Human_jejunum_microvilli_2_-_TEM.jpg/220px-Human_jejunum_microvilli_2_-_TEM.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Human_jejunum_microvilli_2_-_TEM.jpg/330px-Human_jejunum_microvilli_2_-_TEM.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Human_jejunum_microvilli_2_-_TEM.jpg/440px-Human_jejunum_microvilli_2_-_TEM.jpg 2x" data-file-width="640" data-file-height="480" /></a><figcaption><a href="/wiki/Cell_(biology)" title="Cell (biology)">Cells</a> lining the <a href="/wiki/Small_intestine" title="Small intestine">small intestine</a> increase the surface area over which they can absorb nutrients with a carpet of tuftlike <a href="/wiki/Microvilli" class="mw-redirect" title="Microvilli">microvilli</a>.</figcaption></figure> <p>The ratio between the surface area and volume of <a href="/wiki/Cell_(biology)" title="Cell (biology)">cells</a> and <a href="/wiki/Organism" title="Organism">organisms</a> has an enormous impact on their <a href="/wiki/Biology" title="Biology">biology</a>, including their <a href="/wiki/Physiology" title="Physiology">physiology</a> and <a href="/wiki/Behavior" title="Behavior">behavior</a>. For example, many aquatic microorganisms have increased surface area to increase their drag in the water. This reduces their rate of sink and allows them to remain near the surface with less energy expenditure.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2018)">citation needed</span></a></i>]</sup> </p><p>An increased surface area to volume ratio also means increased exposure to the environment. The finely-branched appendages of <a href="/wiki/Filter_feeder" title="Filter feeder">filter feeders</a> such as <a href="/wiki/Krill" title="Krill">krill</a> provide a large surface area to sift the water for food.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Individual organs like the <a href="/wiki/Lung" title="Lung">lung</a> have numerous internal branchings that increase the surface area; in the case of the lung, the large surface supports gas exchange, bringing <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> into the blood and releasing <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a> from the blood.<sup id="cite_ref-tortora1_14-0" class="reference"><a href="#cite_note-tortora1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-grays_15-0" class="reference"><a href="#cite_note-grays-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Similarly, the <a href="/wiki/Small_intestine" title="Small intestine">small intestine</a> has a finely wrinkled internal surface, allowing the body to absorb nutrients efficiently.<sup id="cite_ref-VB_16-0" class="reference"><a href="#cite_note-VB-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Cells can achieve a high surface area to volume ratio with an elaborately convoluted surface, like the <a href="/wiki/Microvilli" class="mw-redirect" title="Microvilli">microvilli</a> lining the <a href="/wiki/Small_intestine" title="Small intestine">small intestine</a>.<sup id="cite_ref-William2005_17-0" class="reference"><a href="#cite_note-William2005-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Increased surface area can also lead to biological problems. More contact with the environment through the surface of a cell or an organ (relative to its volume) increases loss of water and dissolved substances. High surface area to volume ratios also present problems of temperature control in unfavorable environments.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2018)">citation needed</span></a></i>]</sup> </p><p>The surface to volume ratios of organisms of different sizes also leads to some <a href="/wiki/Biological_rule" class="mw-redirect" title="Biological rule">biological rules</a> such as <a href="/wiki/Allen%27s_rule" title="Allen's rule">Allen's rule</a>, <a href="/wiki/Bergmann%27s_rule" title="Bergmann's rule">Bergmann's rule</a><sup id="cite_ref-Meiri2003_18-0" class="reference"><a href="#cite_note-Meiri2003-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Ashton2000_19-0" class="reference"><a href="#cite_note-Ashton2000-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Millien2006_20-0" class="reference"><a href="#cite_note-Millien2006-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Gigantothermy" title="Gigantothermy">gigantothermy</a>.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Fire_spread">Fire spread</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=7" title="Edit section: Fire spread"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the context of <a href="/wiki/Wildfire" title="Wildfire">wildfires</a>, the ratio of the surface area of a solid fuel to its volume is an important measurement. Fire spread behavior is frequently correlated to the surface-area-to-volume ratio of the fuel (e.g. leaves and branches). The higher its value, the faster a particle responds to changes in environmental conditions, such as temperature or moisture. Higher values are also correlated to shorter fuel ignition times, and hence faster fire spread rates. </p> <div class="mw-heading mw-heading3"><h3 id="Planetary_cooling">Planetary cooling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=8" title="Edit section: Planetary cooling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A body of icy or rocky material in outer space may, if it can build and retain sufficient heat, develop a differentiated interior and alter its surface through volcanic or tectonic activity. The length of time through which a planetary body can maintain surface-altering activity depends on how well it retains heat, and this is governed by its surface area-to-volume ratio. For <a href="/wiki/4_Vesta" title="4 Vesta">Vesta</a> (r=263 km), the ratio is so high that astronomers were surprised to find that it <i>did</i> differentiate and have brief volcanic activity. The <a href="/wiki/Moon" title="Moon">moon</a>, <a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a> and <a href="/wiki/Mars" title="Mars">Mars</a> have radii in the low thousands of kilometers; all three retained heat well enough to be thoroughly differentiated although after a billion years or so they became too cool to show anything more than very localized and infrequent volcanic activity. As of April 2019, however, NASA has announced the detection of a "marsquake" measured on April 6, 2019, by NASA's InSight lander.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Venus_(planet)" class="mw-redirect" title="Venus (planet)">Venus</a> and <a href="/wiki/Earth" title="Earth">Earth</a> (r>6,000 km) have sufficiently low surface area-to-volume ratios (roughly half that of Mars and much lower than all other known rocky bodies) so that their heat loss is minimal.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_examples">Mathematical examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=9" title="Edit section: Mathematical examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="List_of_surface-area-to-volume_ratios"></span> </p> <table class="wikitable"> <tbody><tr> <th>Shape </th> <th>Image </th> <th>Characteristic<br />length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" /></span> </th> <th>SA/V ratio </th> <th>SA/V ratio for<br />unit volume </th></tr> <tr> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">Tetrahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Tetrahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/60px-Tetrahedron.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/90px-Tetrahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Tetrahedron.png/120px-Tetrahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>edge </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {6{\sqrt {6}}}{a}}\approx {\frac {14.697}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>14.697</mn> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {6{\sqrt {6}}}{a}}\approx {\frac {14.697}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf1619e0fb3574c7c30cd8674864c81932ad2dcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.491ex; height:5.843ex;" alt="{\displaystyle {\frac {6{\sqrt {6}}}{a}}\approx {\frac {14.697}{a}}}" /></span> </td> <td>7.21 </td></tr> <tr> <td><a href="/wiki/Cube" title="Cube">Cube</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Hexahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/70px-Hexahedron.png" decoding="async" width="70" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/105px-Hexahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/140px-Hexahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>edge </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {6}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>6</mn> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {6}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a27e979d81242392cb3a6097206b51a54098bf42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.066ex; height:5.176ex;" alt="{\displaystyle {\frac {6}{a}}}" /></span> </td> <td>6 </td></tr> <tr> <td><a href="/wiki/Octahedron" title="Octahedron">Octahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Octahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Octahedron.png/70px-Octahedron.png" decoding="async" width="70" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Octahedron.png/105px-Octahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Octahedron.png/140px-Octahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span> </td> <td>edge </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3{\sqrt {6}}}{a}}\approx {\frac {7.348}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>6</mn> </msqrt> </mrow> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7.348</mn> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3{\sqrt {6}}}{a}}\approx {\frac {7.348}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04031270a0bff7d14d7c43d28ba19e7d3818295a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.328ex; height:5.843ex;" alt="{\displaystyle {\frac {3{\sqrt {6}}}{a}}\approx {\frac {7.348}{a}}}" /></span> </td> <td>5.72 </td></tr> <tr> <td><a href="/wiki/Dodecahedron" title="Dodecahedron">Dodecahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Dodecahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/70px-Dodecahedron.png" decoding="async" width="70" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/105px-Dodecahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Dodecahedron.png/140px-Dodecahedron.png 2x" data-file-width="984" data-file-height="951" /></a></span> </td> <td>edge </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {12{\sqrt {25+10{\sqrt {5}}}}}{(15+7{\sqrt {5}})a}}\approx {\frac {2.694}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>12</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>25</mn> <mo>+</mo> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </msqrt> </mrow> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>15</mn> <mo>+</mo> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo stretchy="false">)</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2.694</mn> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {12{\sqrt {25+10{\sqrt {5}}}}}{(15+7{\sqrt {5}})a}}\approx {\frac {2.694}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8367d3bf7bc6484c00fa99de9c615d42e2032ea0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.305ex; height:8.843ex;" alt="{\displaystyle {\frac {12{\sqrt {25+10{\sqrt {5}}}}}{(15+7{\sqrt {5}})a}}\approx {\frac {2.694}{a}}}" /></span> </td> <td>5.31 </td></tr> <tr> <td><a href="/wiki/Capsule_(geometry)" title="Capsule (geometry)">Capsule</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:SA_to_V_shape.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/SA_to_V_shape.png/100px-SA_to_V_shape.png" decoding="async" width="100" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/SA_to_V_shape.png/150px-SA_to_V_shape.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/SA_to_V_shape.png/200px-SA_to_V_shape.png 2x" data-file-width="701" data-file-height="619" /></a></span> </td> <td>radius (R) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {12}{5a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>12</mn> <mrow> <mn>5</mn> <mi>a</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {12}{5a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71f3880000a412c4fd12aadb70569ee0b32d3dc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.228ex; height:5.176ex;" alt="{\displaystyle {\frac {12}{5a}}}" /></span> </td> <td>5.251 </td></tr> <tr> <td><a href="/wiki/Icosahedron" title="Icosahedron">Icosahedron</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Icosahedron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Icosahedron.png/70px-Icosahedron.png" decoding="async" width="70" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Icosahedron.png/105px-Icosahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Icosahedron.png/140px-Icosahedron.png 2x" data-file-width="911" data-file-height="952" /></a></span> </td> <td>edge </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {12{\sqrt {3}}}{(3+{\sqrt {5}})a}}\approx {\frac {3.970}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>12</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo stretchy="false">)</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3.970</mn> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {12{\sqrt {3}}}{(3+{\sqrt {5}})a}}\approx {\frac {3.970}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9656aa95c899e042c5fa53d0aa641dc743b3fb30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.208ex; height:7.009ex;" alt="{\displaystyle {\frac {12{\sqrt {3}}}{(3+{\sqrt {5}})a}}\approx {\frac {3.970}{a}}}" /></span> </td> <td>5.148 </td></tr> <tr> <td><a href="/wiki/Sphere" title="Sphere">Sphere</a> </td> <td><span typeof="mw:File"><a href="/wiki/File:Bump-map-demo-smooth.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Bump-map-demo-smooth.png/70px-Bump-map-demo-smooth.png" decoding="async" width="70" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Bump-map-demo-smooth.png/105px-Bump-map-demo-smooth.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Bump-map-demo-smooth.png/140px-Bump-map-demo-smooth.png 2x" data-file-width="160" data-file-height="160" /></a></span> </td> <td>radius </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b3a1fee962df3ec926c77af1daa6e9bd1d76f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.066ex; height:5.176ex;" alt="{\displaystyle {\frac {3}{a}}}" /></span> </td> <td>4.83598 </td></tr></tbody></table> <table class="wikitable"> <caption>Examples of cubes of different sizes </caption> <tbody><tr> <th>Side of<br />cube</th> <th>Side<sup>2</sup></th> <th>Area of a<br />single face</th> <th>6 × side<sup>2</sup></th> <th>Area of<br />entire cube<br />(6 faces)</th> <th>Side<sup>3</sup></th> <th>Volume</th> <th>Ratio of<br />surface area<br />to volume </th></tr> <tr> <td>2</td> <td>2×2</td> <td>4</td> <td>6×2×2</td> <td>24</td> <td>2×2×2</td> <td>8</td> <td><b>3:1</b> </td></tr> <tr> <td>4</td> <td>4×4</td> <td>16</td> <td>6×4×4</td> <td>96</td> <td>4×4×4</td> <td>64</td> <td><b>3:2</b> </td></tr> <tr> <td>6</td> <td>6×6</td> <td>36</td> <td>6×6×6</td> <td>216</td> <td>6×6×6</td> <td>216</td> <td><b>3:3</b> </td></tr> <tr> <td>8</td> <td>8×8</td> <td>64</td> <td>6×8×8</td> <td>384</td> <td>8×8×8</td> <td>512</td> <td><b>3:4</b> </td></tr> <tr> <td>12</td> <td>12×12</td> <td>144</td> <td>6×12×12</td> <td>864</td> <td>12×12×12</td> <td>1,728</td> <td><b>3:6</b> </td></tr> <tr> <td>20</td> <td>20×20</td> <td>400</td> <td>6×20×20</td> <td>2,400</td> <td>20×20×20</td> <td>8,000</td> <td><b>3:10</b> </td></tr> <tr> <td>50</td> <td>50×50</td> <td>2,500</td> <td>6×50×50</td> <td>15,000</td> <td>50×50×50</td> <td>125,000</td> <td><b>3:25</b> </td></tr> <tr> <td>1,000</td> <td>1,000×1,000</td> <td>1,000,000</td> <td>6×1,000×1,000</td> <td>6,000,000</td> <td>1,000×1,000×1,000</td> <td>1,000,000,000</td> <td><b>3:500</b> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Compactness_measure_of_a_shape" class="mw-redirect" title="Compactness measure of a shape">Compactness measure of a shape</a></li> <li><a href="/wiki/Dust_explosion" title="Dust explosion">Dust explosion</a></li> <li><a href="/wiki/Square%E2%80%93cube_law" title="Square–cube law">Square–cube law</a></li> <li><a href="/wiki/Specific_surface_area" title="Specific surface area">Specific surface area</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite 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New York, NY: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-26657-4" title="Special:BookSources/978-0-521-26657-4"><bdi>978-0-521-26657-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/10697247">10697247</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Scaling%3A+Why+is+Animal+Size+so+Important%3F&rft.place=New+York%2C+NY&rft.pub=Cambridge+University+Press&rft.date=1984&rft_id=info%3Aoclcnum%2F10697247&rft.isbn=978-0-521-26657-4&rft.aulast=Schmidt-Nielsen&rft.aufirst=Knut&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fscalingwhyisanim0000schm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFVogel1988" class="citation book cs1">Vogel, Steven (1988). <i>Life's Devices: The Physical World of Animals and Plants</i>. 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Philadelphia, PA: Holt-Saunders International. pp. <span class="nowrap">349–</span>353. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-03-910284-5" title="Special:BookSources/978-0-03-910284-5"><bdi>978-0-03-910284-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Vertebrate+Body&rft.place=Philadelphia%2C+PA&rft.pages=%3Cspan+class%3D%22nowrap%22%3E349-%3C%2Fspan%3E353&rft.pub=Holt-Saunders+International&rft.date=1977&rft.isbn=978-0-03-910284-5&rft.au=Romer%2C+Alfred+Sherwood&rft.au=Parsons%2C+Thomas+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></span> </li> <li id="cite_note-William2005-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-William2005_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKrause_J._William2005" class="citation book cs1">Krause J. William (July 2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cRayoldYrcUC&pg=PA37"><i>Krause's Essential Human Histology for Medical Students</i></a>. Universal-Publishers. pp. 37–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-58112-468-2" title="Special:BookSources/978-1-58112-468-2"><bdi>978-1-58112-468-2</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">25 November</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Krause%27s+Essential+Human+Histology+for+Medical+Students&rft.pages=37-&rft.pub=Universal-Publishers&rft.date=2005-07&rft.isbn=978-1-58112-468-2&rft.au=Krause+J.+William&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DcRayoldYrcUC%26pg%3DPA37&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></span> </li> <li id="cite_note-Meiri2003-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Meiri2003_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMeiriDayan2003" class="citation journal cs1">Meiri, S.; Dayan, T. (2003-03-20). "On the validity of Bergmann's rule". <i>Journal of Biogeography</i>. <b>30</b> (3): <span class="nowrap">331–</span>351. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003JBiog..30..331M">2003JBiog..30..331M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1046%2Fj.1365-2699.2003.00837.x">10.1046/j.1365-2699.2003.00837.x</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:11954818">11954818</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Biogeography&rft.atitle=On+the+validity+of+Bergmann%27s+rule&rft.volume=30&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E331-%3C%2Fspan%3E351&rft.date=2003-03-20&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A11954818%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1046%2Fj.1365-2699.2003.00837.x&rft_id=info%3Abibcode%2F2003JBiog..30..331M&rft.aulast=Meiri&rft.aufirst=S.&rft.au=Dayan%2C+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></span> </li> <li id="cite_note-Ashton2000-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ashton2000_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAshtonTracyQueiroz2000" class="citation journal cs1">Ashton, Kyle G.; Tracy, Mark C.; Queiroz, Alan de (October 2000). "Is Bergmann's Rule Valid for Mammals?". <i><a href="/wiki/The_American_Naturalist" title="The American Naturalist">The American Naturalist</a></i>. <b>156</b> (4): <span class="nowrap">390–</span>415. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F303400">10.1086/303400</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/10.1086/303400">10.1086/303400</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/29592141">29592141</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:205983729">205983729</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Naturalist&rft.atitle=Is+Bergmann%27s+Rule+Valid+for+Mammals%3F&rft.volume=156&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E390-%3C%2Fspan%3E415&rft.date=2000-10&rft_id=info%3Apmid%2F29592141&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A205983729%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F10.1086%2F303400%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1086%2F303400&rft.aulast=Ashton&rft.aufirst=Kyle+G.&rft.au=Tracy%2C+Mark+C.&rft.au=Queiroz%2C+Alan+de&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></span> </li> <li id="cite_note-Millien2006-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Millien2006_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMillienLyonsOlson2006" class="citation journal cs1">Millien, Virginie; Lyons, S. Kathleen; Olson, Link; et al. (May 23, 2006). "Ecotypic variation in the context of global climate change: Revisiting the rules". <i><a href="/wiki/Ecology_Letters" title="Ecology Letters">Ecology Letters</a></i>. <b>9</b> (7): <span class="nowrap">853–</span>869. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006EcolL...9..853M">2006EcolL...9..853M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1461-0248.2006.00928.x">10.1111/j.1461-0248.2006.00928.x</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16796576">16796576</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ecology+Letters&rft.atitle=Ecotypic+variation+in+the+context+of+global+climate+change%3A+Revisiting+the+rules&rft.volume=9&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E853-%3C%2Fspan%3E869&rft.date=2006-05-23&rft_id=info%3Apmid%2F16796576&rft_id=info%3Adoi%2F10.1111%2Fj.1461-0248.2006.00928.x&rft_id=info%3Abibcode%2F2006EcolL...9..853M&rft.aulast=Millien&rft.aufirst=Virginie&rft.au=Lyons%2C+S.+Kathleen&rft.au=Olson%2C+Link&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFitzpatrick2005" class="citation web cs1">Fitzpatrick, Katie (2005). <a rel="nofollow" class="external text" href="https://archive.today/20120630084621/http://www.bio.davidson.edu/people/midorcas/animalphysiology/websites/2005/Fitzpatrick/Gigantothermy.htm">"Gigantothermy"</a>. <a href="/wiki/Davidson_College" title="Davidson College">Davidson College</a>. Archived from <a rel="nofollow" class="external text" href="http://www.bio.davidson.edu/people/midorcas/animalphysiology/websites/2005/Fitzpatrick/Gigantothermy.htm">the original</a> on 2012-06-30<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-12-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Gigantothermy&rft.pub=Davidson+College&rft.date=2005&rft.aulast=Fitzpatrick&rft.aufirst=Katie&rft_id=http%3A%2F%2Fwww.bio.davidson.edu%2Fpeople%2Fmidorcas%2Fanimalphysiology%2Fwebsites%2F2005%2FFitzpatrick%2FGigantothermy.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.space.com/insight-mars-lander-first-marsquake.html">"Marsquake! NASA's InSight Lander Feels Its 1st Red Planet Tremor"</a>. <i><a href="/wiki/Space.com" title="Space.com">Space.com</a></i>. 23 April 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Space.com&rft.atitle=Marsquake%21+NASA%27s+InSight+Lander+Feels+Its+1st+Red+Planet+Tremor&rft.date=2019-04-23&rft_id=https%3A%2F%2Fwww.space.com%2Finsight-mars-lander-first-marsquake.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180613195628/http://www.astro.uvic.ca/~venn/A201/maths.6.planetary_cooling.pdf">"Archived copy"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.astro.uvic.ca/~venn/A201/maths.6.planetary_cooling.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2018-06-13<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-08-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archived+copy&rft_id=http%3A%2F%2Fwww.astro.uvic.ca%2F~venn%2FA201%2Fmaths.6.planetary_cooling.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface-area-to-volume+ratio" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_web" title="Template:Cite web">cite web</a>}}</code>: CS1 maint: archived copy as title (<a href="/wiki/Category:CS1_maint:_archived_copy_as_title" title="Category:CS1 maint: archived copy as title">link</a>)</span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.tiem.utk.edu/~gross/bioed/bealsmodules/area_volume.html">Sizes of Organisms: The Surface Area:Volume Ratio</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170814195742/http://www.tiem.utk.edu/~gross/bioed/bealsmodules/area_volume.html">Archived</a> 2017-08-14 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140310230709/http://www.nwcg.gov/var/glossary/surface-area-to-volume-ratio">National Wildfire Coordinating Group: Surface Area to Volume Ratio</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140521215017/http://www.nwcg.gov/pms/RxFire/FEG.pdf">Previous link not working, references are in this document, PDF</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface-area-to-volume_ratio&action=edit&section=13" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://irl.cs.ucla.edu/papers/right-size.html">On Being the Right Size, J.B.S. Haldane</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110822151104/http://irl.cs.ucla.edu/papers/right-size.html">Archived</a> 2011-08-22 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Surface-area-to-volume_ratio&oldid=1270451795">https://en.wikipedia.org/w/index.php?title=Surface-area-to-volume_ratio&oldid=1270451795</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Chemical_kinetics" title="Category:Chemical kinetics">Chemical kinetics</a></li><li><a href="/wiki/Category:Cell_biology" title="Category:Cell biology">Cell biology</a></li><li><a href="/wiki/Category:Physiology" title="Category:Physiology">Physiology</a></li><li><a href="/wiki/Category:Ratios" title="Category:Ratios">Ratios</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_maint:_archived_copy_as_title" title="Category:CS1 maint: archived copy as title">CS1 maint: archived copy as title</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_February_2014" title="Category:Articles needing additional references from February 2014">Articles needing additional references from February 2014</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_January_2018" title="Category:Articles with unsourced statements from January 2018">Articles with unsourced statements from January 2018</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 19 January 2025, at 16:11<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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