20:
818:
1469:
932:, 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.
716:
1325:
1218:
1030:
1378:
1148:
1100:
131:
110:
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
940:
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
961:
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
900:
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
31:
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)
111:
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", and elsewhere.
1309:
686:
692:
For a given shape, SA:V is inversely proportional to size. A cube 2 cm on a side has a ratio of 3 cm, half that of a cube 1 cm on a side. Conversely, preserving SA:V as size increases requires changing to a less
1453:
856:. 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.
1084:
1202:
495:
395:
970:(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.
270:
2641:
1362:
215:
1501:
1132:
548:
1228:
798:) 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,
71:
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
590:
2595:
Millien, Virginie; Lyons, S. Kathleen; Olson, Link; et al. (May 23, 2006). "Ecotypic variation in the context of global climate change: Revisiting the rules".
2108:"Scaffolds with a High Surface Area-to-Volume Ratio and Cultured Under Fast Flow Perfusion Result in Optimal O2 Delivery to the Cells in Artificial Bone Tissues"
1009:
2365:
550:. Thus, the same linear relationship between area and volume holds for any number of dimensions (see figure): doubling the radius always halves the ratio.
1388:
173:
For an ordinary three-dimensional ball, the SA:V can be calculated using the standard equations for the surface and volume, which are, respectively,
2298:"General models for the spectra of surface area scaling strategies of cells and organisms: fractality, geometric dissimilitude, and internalization"
309:
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:
119:
2740:
2690:
134:
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.
107:, design of artificial bone tissue, artificial lungs and many more biological and biotechnological structures. For more examples see Glazier.
874:
have numerous internal branchings that increase the surface area; in the case of the lung, the large surface supports gas exchange, bringing
737:
2749:
2649:
1040:
1158:
2721:
401:
315:
859:
An increased surface area to volume ratio also means increased exposure to the environment. The finely-branched appendages of
2476:
2449:
2399:
1854:
1827:
2769:
805:
A high surface area to volume ratio provides a strong "driving force" to speed up thermodynamic processes that minimize
2259:
2249:
763:
2754:
2372:", Proceedings of the Seminar and Report of Krill Ecology Group, Editor S. B. Schnack, 130-155 and title page image.
745:
584:
will have a surface area of 6 cm and a volume of 1 cm. The surface to volume ratio for this cube is thus
2424:
2352:
1786:
795:
741:
694:
2542:
Ashton, Kyle G.; Tracy, Mark C.; Queiroz, Alan de (October 2000). "Is
Bergmann's Rule Valid for Mammals?".
2192:
114:
For a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is a
220:
2788:
889:
Cells can achieve a high surface area to volume ratio with an elaborately convoluted surface, like the
280:, in an inverse relationship with the radius - if the radius is doubled, the SA:V halves (see figure).
1335:
122:. By contrast, objects with acute-angled spikes will have very large surface area for a given volume.
2737:
1940:
1886:
806:
176:
2697:
1479:
1304:{\displaystyle {\frac {12{\sqrt {25+10{\sqrt {5}}}}}{(15+7{\sqrt {5}})a}}\approx {\frac {2.694}{a}}}
1110:
726:
503:
2670:
2544:
730:
151:
19:
1941:"The surface-to-volume ratio in thermal physics: from cheese cube physics to animal metabolism"
1887:"The surface-to-volume ratio in thermal physics: from cheese cube physics to animal metabolism"
681:{\displaystyle {\mbox{SA:V}}={\frac {6~{\mbox{cm}}^{2}}{1~{\mbox{cm}}^{3}}}=6~{\mbox{cm}}^{-1}}
2391:
2793:
2466:
1801:
2606:
2508:
2106:
Nguyen, Thanh Danh; Olufemi E., Kadri; Vassilios I., Sikavitsas; Voronov, Roman S. (2019).
1952:
1898:
886:
has a finely wrinkled internal surface, allowing the body to absorb nutrients efficiently.
566:
8:
2798:
1796:
828:
increase the surface area over which they can absorb nutrients with a carpet of tuftlike
799:
2610:
2512:
2001:
Jeremy M., Howard; Hannah-Beth, Griffis; Westendorf, Rachel; Williams, Jason B. (2019).
1956:
1902:
2577:
2561:
2524:
2333:
2274:
2220:
2170:
2068:
2043:
1968:
1914:
1816:
1318:
994:
913:
559:
145:
88:
945:(r=263 km), the ratio is so high that astronomers were surprised to find that it
2715:
2622:
2618:
2581:
2569:
2520:
2472:
2445:
2420:
2395:
2384:
2325:
2317:
2255:
2245:
2239:
2212:
2208:
2162:
2073:
2024:
1964:
1910:
1860:
1850:
1833:
1823:
2528:
2337:
2224:
2174:
1972:
1918:
2645:
2614:
2553:
2516:
2309:
2204:
2152:
2119:
2063:
2055:
2014:
1960:
1906:
1448:{\displaystyle {\frac {12{\sqrt {3}}}{(3+{\sqrt {5}})a}}\approx {\frac {3.970}{a}}}
954:
817:
104:
2803:
2773:
2744:
2597:
2419:(Thirty-seventh ed.). Edinburgh: Churchill Livingstone. pp. 1278–1282.
2157:
2140:
909:
905:
894:
883:
825:
2766:
962:
detection of a "marsquake" measured on April 6, 2019, by NASA's InSight lander.
904:
The surface to volume ratios of organisms of different sizes also leads to some
2415:
Williams, Peter L; Warwick, Roger; Dyson, Mary; Bannister, Lawrence H. (1989).
1791:
963:
941:
it retains heat, and this is governed by its surface area-to-volume ratio. For
879:
837:
821:
777:
562:
96:
2565:
2357:- some outstanding energetics and dynamics - some unique morphological details
2059:
2044:"Surface Area to Volume Ratio: A Natural Variable for Bacterial Morphogenesis"
2782:
2321:
2019:
2002:
1986:
Williams, Peter; Warwick, Roger; Dyson, Mary; Bannister, Lawrence H. (2005).
917:
860:
573:
84:
76:
2297:
2193:"A unifying explanation for diverse metabolic scaling in animals and plants"
1864:
1837:
75:
the volume. Good examples for such processes are processes governed by the
2626:
2573:
2329:
2216:
2166:
2077:
2028:
1211:
783:
155:
140:
61:
2499:
Meiri, S.; Dayan, T. (2003-03-20). "On the validity of
Bergmann's rule".
1371:
1023:
570:
2439:
2238:
Alberts, Bruce (2002). "The
Diversity of Genomes and the Tree of Life".
2124:
2107:
1468:
1141:
890:
849:
829:
581:
2000:
2675:
2275:"What's Your Sphericity Index? Rationalizing Surface Area and Volume"
80:
1945:
European
Journal of Physics European Physical Society, Find Out More
1079:{\displaystyle {\frac {6{\sqrt {6}}}{a}}\approx {\frac {14.697}{a}}}
715:
2557:
2444:. Philadelphia, PA: Holt-Saunders International. pp. 349–353.
2390:(Fifth ed.). New York: Harper & Row, Publishers. pp.
2313:
2105:
2003:"The influence of size and abiotic factors on cutaneous water loss"
1197:{\displaystyle {\frac {3{\sqrt {6}}}{a}}\approx {\frac {7.348}{a}}}
929:
853:
841:
802:. Finely ground salt dissolves much more quickly than coarse salt.
791:
2750:
National
Wildfire Coordinating Group: Surface Area to Volume Ratio
2671:"Marsquake! NASA's InSight Lander Feels Its 1st Red Planet Tremor"
942:
845:
490:{\displaystyle SA={\frac {nr^{n-1}\pi ^{n/2}}{\Gamma (1+{n/2})}}}
91:. SA:V is used to explain the diffusion of small molecules, like
1324:
2755:
Previous link not working, references are in this document, PDF
1462:
1217:
875:
787:
294:
167:
159:
115:
92:
65:
1377:
1029:
2414:
1985:
1147:
1099:
967:
864:
100:
57:
2141:"Microchannel Technologies for Artificial Lungs: (1) Theory"
276:= 1 the SA:V is thus 3. For the general case, SA:V equals 3/
166:
properly refers only to the surface, so a sphere thus lacks
1093:
958:
950:
871:
577:
390:{\displaystyle V={\frac {r^{n}\pi ^{n/2}}{\Gamma (1+n/2)}}}
1990:(39 ed.). Churchill Livingstone. pp. 1278–1282.
1885:
Planinšič, Gorazd; Vollmer, Michael (February 20, 2008).
867:
provide a large surface area to sift the water for food.
130:
1847:
Life's
Devices: The Physical World of Animals and Plants
292:
Balls exist in any dimension and are generically called
2468:
Krause's
Essential Human Histology for Medical Students
2382:
Tortora, Gerard J.; Anagnostakos, Nicholas P. (1987).
2366:
Alfred
Wegener Institute for Polar and Marine Research
663:
637:
615:
595:
1482:
1391:
1338:
1231:
1161:
1113:
1043:
997:
593:
506:
404:
318:
223:
179:
103:
loss by animals, bacterial morphogenesis, organism's
949:
differentiate and have brief volcanic activity. The
2440:Romer, Alfred Sherwood; Parsons, Thomas S. (1977).
2381:
2368:, Special Issue 4 (1983): "On the biology of Krill
2541:
2383:
1815:
1495:
1447:
1356:
1303:
1196:
1126:
1078:
1003:
680:
542:
489:
389:
264:
209:
2738:Sizes of Organisms: The Surface Area:Volume Ratio
2594:
2464:
836:The ratio between the surface area and volume of
2780:
1884:
2139:J. K, Lee; H. H., Kung; L. F., Mockros (2008).
1813:
2138:
2041:
1849:. Princeton, NJ: Princeton University Press.
2042:Harris, Leigh K.; Theriot, Julie A. (2018).
1822:. New York, NY: Cambridge University Press.
2639:
2588:
2458:
744:. Unsourced material may be challenged and
2535:
2498:
2241:Molecular Biology of the Cell, 4th edition
283:
2492:
2353:Swimming and feeding of Antarctic Krill,
2156:
2123:
2067:
2018:
1938:
1818:Scaling: Why is Animal Size so Important?
764:Learn how and when to remove this message
2375:
973:
816:
129:
120:isoperimetric inequality in 3 dimensions
18:
2767:On Being the Right Size, J.B.S. Haldane
2237:
2190:
68:of an object or collection of objects.
2781:
2720:: CS1 maint: archived copy as title (
2471:. Universal-Publishers. pp. 37–.
790:ratio (e.g. very small diameter, very
553:
2408:
1844:
1512:Examples of cubes of different sizes
705:
558:The surface-area-to-volume ratio has
2386:Principles of anatomy and physiology
2295:
2272:
2186:
2184:
2090:
935:
742:adding citations to reliable sources
709:
576:and submultiples. As an example, a
125:
13:
2760:
2433:
565:(L) and is therefore expressed in
456:
358:
265:{\displaystyle V=(4/3)\pi {r^{3}}}
14:
2815:
2731:
2181:
2619:10.1111/j.1461-0248.2006.00928.x
2521:10.1046/j.1365-2699.2003.00837.x
2209:10.1111/j.1469-185X.2009.00095.x
2007:Advances in Physiology Education
1467:
1376:
1357:{\displaystyle {\frac {12}{5a}}}
1323:
1216:
1146:
1098:
1028:
844:has an enormous impact on their
714:
2683:
2663:
2633:
2465:Krause J. William (July 2005).
2344:
2289:
2266:
2231:
882:from the blood. Similarly, the
700:
210:{\displaystyle SA=4\pi {r^{2}}}
2296:Okie, Jordan G. (March 2013).
2132:
2099:
2084:
2035:
1994:
1979:
1932:
1878:
1814:Schmidt-Nielsen, Knut (1984).
1787:Compactness measure of a shape
1496:{\displaystyle {\frac {3}{a}}}
1423:
1407:
1279:
1260:
1127:{\displaystyle {\frac {6}{a}}}
923:
481:
459:
381:
361:
244:
230:
99:between air, blood and cells,
1:
2244:. New York: Garland Science.
1807:
878:into the blood and releasing
272:. For the unit case in which
2279:Virginia Mathematics Teacher
2191:Glazier, Douglas S. (2010).
2158:10.1097/MAT.0b013e31817ed9e1
2093:Physiological Animal Ecology
580:with sides of length 1
569:of inverse metre (m) or its
543:{\displaystyle SA/V=nr^{-1}}
38:surface-area-to-volume ratio
16:Surface area per unit volume
7:
2640:Fitzpatrick, Katie (2005).
2362:Berichte zur Polarforschung
1891:European Journal of Physics
1780:
870:Individual organs like the
10:
2820:
1965:10.1088/0143-0807/29/2/017
1939:Planinšič, Gorazd (2008).
1911:10.1088/0143-0807/29/2/017
901:unfavorable environments.
812:
775:
2273:Adam, John (2020-01-01).
2060:10.1016/j.tim.2018.04.008
162:. (In geometry, the term
2091:Louw, Gideon N. (1993).
2020:10.1152/advan.00152.2019
23:Graphs of surface area,
2545:The American Naturalist
2501:Journal of Biogeography
2302:The American Naturalist
800:grain dust is explosive
118:, a consequence of the
42:surface-to-volume ratio
2048:Trends in Microbiology
1845:Vogel, Steven (1988).
1497:
1449:
1358:
1305:
1198:
1128:
1080:
1005:
833:
682:
544:
491:
391:
266:
211:
135:
33:
1802:Specific surface area
1498:
1450:
1359:
1306:
1199:
1129:
1081:
1006:
974:Mathematical examples
820:
683:
545:
492:
392:
267:
212:
133:
22:
2095:. Longman Pub Group.
1480:
1389:
1336:
1229:
1159:
1111:
1041:
995:
782:Materials with high
738:improve this section
591:
504:
500:So the ratio equals
402:
316:
221:
177:
2611:2006EcolL...9..853M
2513:2003JBiog..30..331M
2442:The Vertebrate Body
1957:2008EJPh...29..369P
1903:2008EJPh...29..369P
1513:
794:, or otherwise not
554:Dimension and units
170:in this context.)
2772:2011-08-22 at the
2743:2017-08-14 at the
2197:Biological Reviews
2125:10.3390/app9112381
1511:
1493:
1445:
1354:
1301:
1194:
1124:
1076:
1001:
928:In the context of
848:, including their
834:
706:Physical chemistry
678:
667:
641:
619:
599:
560:physical dimension
540:
487:
387:
288:-dimensional balls
262:
207:
154:object, being the
136:
89:thermal conduction
34:
2789:Chemical kinetics
2478:978-1-58112-468-2
2451:978-0-03-910284-5
2401:978-0-06-350729-6
2370:Euphausia superba
2355:Euphausia superba
1856:978-0-691-08504-3
1829:978-0-521-26657-4
1778:
1777:
1766:1,000Ă—1,000Ă—1,000
1509:
1508:
1491:
1443:
1430:
1421:
1403:
1352:
1299:
1286:
1277:
1256:
1254:
1192:
1179:
1173:
1122:
1074:
1061:
1055:
1004:{\displaystyle a}
936:Planetary cooling
774:
773:
766:
666:
660:
650:
640:
634:
618:
612:
598:
485:
385:
152:three-dimensional
126:For solid spheres
2811:
2726:
2725:
2719:
2711:
2709:
2708:
2702:
2696:. Archived from
2695:
2687:
2681:
2680:
2679:. 23 April 2019.
2667:
2661:
2660:
2658:
2657:
2648:. Archived from
2646:Davidson College
2637:
2631:
2630:
2592:
2586:
2585:
2539:
2533:
2532:
2496:
2490:
2489:
2487:
2485:
2462:
2456:
2455:
2437:
2431:
2430:
2412:
2406:
2405:
2389:
2379:
2373:
2348:
2342:
2341:
2293:
2287:
2286:
2270:
2264:
2263:
2235:
2229:
2228:
2188:
2179:
2178:
2160:
2136:
2130:
2129:
2127:
2112:Applied Sciences
2103:
2097:
2096:
2088:
2082:
2081:
2071:
2039:
2033:
2032:
2022:
1998:
1992:
1991:
1983:
1977:
1976:
1936:
1930:
1929:
1927:
1925:
1882:
1868:
1841:
1821:
1514:
1510:
1502:
1500:
1499:
1494:
1492:
1484:
1471:
1454:
1452:
1451:
1446:
1444:
1436:
1431:
1429:
1422:
1417:
1405:
1404:
1399:
1393:
1380:
1363:
1361:
1360:
1355:
1353:
1351:
1340:
1327:
1310:
1308:
1307:
1302:
1300:
1292:
1287:
1285:
1278:
1273:
1258:
1257:
1255:
1250:
1239:
1233:
1220:
1203:
1201:
1200:
1195:
1193:
1185:
1180:
1175:
1174:
1169:
1163:
1150:
1133:
1131:
1130:
1125:
1123:
1115:
1102:
1085:
1083:
1082:
1077:
1075:
1067:
1062:
1057:
1056:
1051:
1045:
1032:
1010:
1008:
1007:
1002:
980:
979:
906:biological rules
769:
762:
758:
755:
749:
718:
710:
687:
685:
684:
679:
677:
676:
668:
664:
658:
651:
649:
648:
647:
642:
638:
632:
627:
626:
625:
620:
616:
610:
605:
600:
596:
549:
547:
546:
541:
539:
538:
517:
496:
494:
493:
488:
486:
484:
480:
476:
454:
453:
452:
448:
435:
434:
415:
396:
394:
393:
388:
386:
384:
377:
356:
355:
354:
350:
337:
336:
326:
271:
269:
268:
263:
261:
260:
259:
240:
216:
214:
213:
208:
206:
205:
204:
105:thermoregulation
27:against volume,
2819:
2818:
2814:
2813:
2812:
2810:
2809:
2808:
2779:
2778:
2774:Wayback Machine
2763:
2761:Further reading
2745:Wayback Machine
2734:
2729:
2713:
2712:
2706:
2704:
2700:
2693:
2691:"Archived copy"
2689:
2688:
2684:
2669:
2668:
2664:
2655:
2653:
2642:"Gigantothermy"
2638:
2634:
2598:Ecology Letters
2593:
2589:
2540:
2536:
2497:
2493:
2483:
2481:
2479:
2463:
2459:
2452:
2438:
2434:
2427:
2413:
2409:
2402:
2380:
2376:
2349:
2345:
2294:
2290:
2271:
2267:
2252:
2236:
2232:
2189:
2182:
2137:
2133:
2104:
2100:
2089:
2085:
2054:(10): 815–832.
2040:
2036:
1999:
1995:
1984:
1980:
1937:
1933:
1923:
1921:
1883:
1879:
1857:
1830:
1810:
1797:Square–cube law
1783:
1549:
1547:
1536:
1534:
1526:
1518:
1483:
1481:
1478:
1477:
1435:
1416:
1406:
1398:
1394:
1392:
1390:
1387:
1386:
1344:
1339:
1337:
1334:
1333:
1291:
1272:
1259:
1249:
1238:
1234:
1232:
1230:
1227:
1226:
1184:
1168:
1164:
1162:
1160:
1157:
1156:
1114:
1112:
1109:
1108:
1066:
1050:
1046:
1044:
1042:
1039:
1038:
1017:
996:
993:
992:
990:
976:
938:
926:
914:Bergmann's rule
895:small intestine
884:small intestine
826:small intestine
815:
780:
770:
759:
753:
750:
735:
719:
708:
703:
669:
662:
661:
643:
636:
635:
628:
621:
614:
613:
606:
604:
594:
592:
589:
588:
556:
531:
527:
513:
505:
502:
501:
472:
468:
455:
444:
440:
436:
424:
420:
416:
414:
403:
400:
399:
373:
357:
346:
342:
338:
332:
328:
327:
325:
317:
314:
313:
290:
255:
251:
250:
236:
222:
219:
218:
200:
196:
195:
178:
175:
174:
128:
17:
12:
11:
5:
2817:
2807:
2806:
2801:
2796:
2791:
2777:
2776:
2762:
2759:
2758:
2757:
2752:
2747:
2733:
2732:External links
2730:
2728:
2727:
2682:
2662:
2632:
2605:(7): 853–869.
2587:
2566:10.1086/303400
2558:10.1086/303400
2552:(4): 390–415.
2534:
2507:(3): 331–351.
2491:
2477:
2457:
2450:
2432:
2425:
2417:Gray's Anatomy
2407:
2400:
2374:
2343:
2314:10.1086/669150
2308:(3): 421–439.
2288:
2265:
2250:
2230:
2203:(1): 111–138.
2180:
2151:(4): 372–382.
2131:
2098:
2083:
2034:
2013:(3): 387–393.
1993:
1988:Gray's Anatomy
1978:
1951:(2): 369–384.
1931:
1897:(2): 369–384.
1876:
1875:
1874:
1870:
1869:
1855:
1842:
1828:
1809:
1806:
1805:
1804:
1799:
1794:
1792:Dust explosion
1789:
1782:
1779:
1776:
1775:
1770:
1767:
1764:
1761:
1758:
1755:
1752:
1748:
1747:
1742:
1739:
1736:
1733:
1730:
1727:
1724:
1720:
1719:
1714:
1711:
1708:
1705:
1702:
1699:
1696:
1692:
1691:
1686:
1683:
1680:
1677:
1674:
1671:
1668:
1664:
1663:
1658:
1655:
1652:
1649:
1646:
1643:
1640:
1636:
1635:
1630:
1627:
1624:
1621:
1618:
1615:
1612:
1608:
1607:
1602:
1599:
1596:
1593:
1590:
1587:
1584:
1580:
1579:
1574:
1571:
1568:
1565:
1562:
1559:
1556:
1552:
1551:
1544:
1541:
1538:
1531:
1528:
1523:
1520:
1507:
1506:
1503:
1490:
1487:
1475:
1472:
1465:
1459:
1458:
1455:
1442:
1439:
1434:
1428:
1425:
1420:
1415:
1412:
1409:
1402:
1397:
1384:
1381:
1374:
1368:
1367:
1364:
1350:
1347:
1343:
1331:
1328:
1321:
1315:
1314:
1311:
1298:
1295:
1290:
1284:
1281:
1276:
1271:
1268:
1265:
1262:
1253:
1248:
1245:
1242:
1237:
1224:
1221:
1214:
1208:
1207:
1204:
1191:
1188:
1183:
1178:
1172:
1167:
1154:
1151:
1144:
1138:
1137:
1134:
1121:
1118:
1106:
1103:
1096:
1090:
1089:
1086:
1073:
1070:
1065:
1060:
1054:
1049:
1036:
1033:
1026:
1020:
1019:
1016:SA/V ratio for
1014:
1011:
1000:
989:Characteristic
987:
984:
975:
972:
937:
934:
925:
922:
880:carbon dioxide
861:filter feeders
814:
811:
778:Dust explosion
772:
771:
722:
720:
713:
707:
704:
702:
699:
690:
689:
675:
672:
657:
654:
646:
631:
624:
609:
603:
574:unit multiples
563:inverse length
555:
552:
537:
534:
530:
526:
523:
520:
516:
512:
509:
498:
497:
483:
479:
475:
471:
467:
464:
461:
458:
451:
447:
443:
439:
433:
430:
427:
423:
419:
413:
410:
407:
397:
383:
380:
376:
372:
369:
366:
363:
360:
353:
349:
345:
341:
335:
331:
324:
321:
289:
282:
258:
254:
249:
246:
243:
239:
235:
232:
229:
226:
203:
199:
194:
191:
188:
185:
182:
127:
124:
97:carbon dioxide
74:
15:
9:
6:
4:
3:
2:
2816:
2805:
2802:
2800:
2797:
2795:
2792:
2790:
2787:
2786:
2784:
2775:
2771:
2768:
2765:
2764:
2756:
2753:
2751:
2748:
2746:
2742:
2739:
2736:
2735:
2723:
2717:
2703:on 2018-06-13
2699:
2692:
2686:
2678:
2677:
2672:
2666:
2652:on 2012-06-30
2651:
2647:
2643:
2636:
2628:
2624:
2620:
2616:
2612:
2608:
2604:
2600:
2599:
2591:
2583:
2579:
2575:
2571:
2567:
2563:
2559:
2555:
2551:
2547:
2546:
2538:
2530:
2526:
2522:
2518:
2514:
2510:
2506:
2502:
2495:
2480:
2474:
2470:
2469:
2461:
2453:
2447:
2443:
2436:
2428:
2422:
2418:
2411:
2403:
2397:
2393:
2388:
2387:
2378:
2371:
2367:
2363:
2359:
2358:
2356:
2347:
2339:
2335:
2331:
2327:
2323:
2319:
2315:
2311:
2307:
2303:
2299:
2292:
2284:
2280:
2276:
2269:
2261:
2260:0-8153-4072-9
2257:
2253:
2251:0-8153-3218-1
2247:
2243:
2242:
2234:
2226:
2222:
2218:
2214:
2210:
2206:
2202:
2198:
2194:
2187:
2185:
2176:
2172:
2168:
2164:
2159:
2154:
2150:
2146:
2145:ASAIO Journal
2142:
2135:
2126:
2121:
2117:
2113:
2109:
2102:
2094:
2087:
2079:
2075:
2070:
2065:
2061:
2057:
2053:
2049:
2045:
2038:
2030:
2026:
2021:
2016:
2012:
2008:
2004:
1997:
1989:
1982:
1974:
1970:
1966:
1962:
1958:
1954:
1950:
1946:
1942:
1935:
1920:
1916:
1912:
1908:
1904:
1900:
1896:
1892:
1888:
1881:
1877:
1872:
1871:
1866:
1862:
1858:
1852:
1848:
1843:
1839:
1835:
1831:
1825:
1820:
1819:
1812:
1811:
1803:
1800:
1798:
1795:
1793:
1790:
1788:
1785:
1784:
1774:
1771:
1769:1,000,000,000
1768:
1765:
1762:
1760:6Ă—1,000Ă—1,000
1759:
1756:
1753:
1750:
1749:
1746:
1743:
1740:
1737:
1734:
1731:
1728:
1725:
1722:
1721:
1718:
1715:
1712:
1709:
1706:
1703:
1700:
1697:
1694:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1669:
1666:
1665:
1662:
1659:
1656:
1653:
1650:
1647:
1644:
1641:
1638:
1637:
1634:
1631:
1628:
1625:
1622:
1619:
1616:
1613:
1610:
1609:
1606:
1603:
1600:
1597:
1594:
1591:
1588:
1585:
1582:
1581:
1578:
1575:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1553:
1545:
1542:
1539:
1532:
1529:
1524:
1521:
1516:
1515:
1504:
1488:
1485:
1476:
1473:
1470:
1466:
1464:
1461:
1460:
1456:
1440:
1437:
1432:
1426:
1418:
1413:
1410:
1400:
1395:
1385:
1382:
1379:
1375:
1373:
1370:
1369:
1365:
1348:
1345:
1341:
1332:
1329:
1326:
1322:
1320:
1317:
1316:
1312:
1296:
1293:
1288:
1282:
1274:
1269:
1266:
1263:
1251:
1246:
1243:
1240:
1235:
1225:
1222:
1219:
1215:
1213:
1210:
1209:
1205:
1189:
1186:
1181:
1176:
1170:
1165:
1155:
1152:
1149:
1145:
1143:
1140:
1139:
1135:
1119:
1116:
1107:
1104:
1101:
1097:
1095:
1092:
1091:
1087:
1071:
1068:
1063:
1058:
1052:
1047:
1037:
1034:
1031:
1027:
1025:
1022:
1021:
1015:
1012:
998:
988:
985:
982:
981:
978:
971:
969:
965:
960:
956:
952:
948:
944:
933:
931:
921:
919:
918:gigantothermy
915:
911:
907:
902:
898:
896:
892:
887:
885:
881:
877:
873:
868:
866:
862:
857:
855:
851:
847:
843:
839:
831:
827:
823:
819:
810:
808:
803:
801:
797:
793:
789:
785:
779:
768:
765:
757:
754:February 2014
747:
743:
739:
733:
732:
728:
723:This section
721:
717:
712:
711:
698:
696:
673:
670:
655:
652:
644:
629:
622:
607:
601:
587:
586:
585:
583:
579:
575:
572:
568:
564:
561:
551:
535:
532:
528:
524:
521:
518:
514:
510:
507:
477:
473:
469:
465:
462:
449:
445:
441:
437:
431:
428:
425:
421:
417:
411:
408:
405:
398:
378:
374:
370:
367:
364:
351:
347:
343:
339:
333:
329:
322:
319:
312:
311:
310:
308:
304:
300:
299:
297:
287:
281:
279:
275:
256:
252:
247:
241:
237:
233:
227:
224:
201:
197:
192:
189:
186:
183:
180:
171:
169:
165:
161:
158:bounded by a
157:
153:
149:
148:
143:
142:
132:
123:
121:
117:
112:
108:
106:
102:
98:
94:
90:
86:
85:heat transfer
82:
78:
77:heat equation
72:
69:
67:
63:
59:
55:
51:
47:
43:
39:
30:
26:
21:
2794:Cell biology
2705:. Retrieved
2698:the original
2685:
2674:
2665:
2654:. Retrieved
2650:the original
2635:
2602:
2596:
2590:
2549:
2543:
2537:
2504:
2500:
2494:
2482:. Retrieved
2467:
2460:
2441:
2435:
2416:
2410:
2385:
2377:
2369:
2361:
2354:
2351:
2346:
2305:
2301:
2291:
2282:
2278:
2268:
2240:
2233:
2200:
2196:
2148:
2144:
2134:
2118:(11): 2381.
2115:
2111:
2101:
2092:
2086:
2051:
2047:
2037:
2010:
2006:
1996:
1987:
1981:
1948:
1944:
1934:
1922:. Retrieved
1894:
1890:
1880:
1846:
1817:
1772:
1744:
1716:
1688:
1660:
1632:
1604:
1576:
1548:surface area
1212:Dodecahedron
1018:unit volume
977:
946:
939:
927:
910:Allen's rule
903:
899:
888:
869:
858:
835:
804:
784:surface area
781:
760:
751:
736:Please help
724:
701:Applications
691:
557:
499:
306:
302:
295:
293:
291:
285:
277:
273:
172:
163:
156:solid figure
146:
141:solid sphere
139:
137:
113:
109:
70:
62:surface area
53:
49:
45:
44:(denoted as
41:
37:
35:
28:
24:
2484:25 November
2426:0443-041776
1754:1,000Ă—1,000
1535:entire cube
1527:single face
1372:Icosahedron
1330:radius (R)
1024:Tetrahedron
1013:SA/V ratio
924:Fire spread
893:lining the
824:lining the
807:free energy
79:, that is,
2799:Physiology
2783:Categories
2707:2018-08-22
2656:2011-12-21
2350:Kils, U.:
1808:References
1550:to volume
1142:Octahedron
891:microvilli
850:physiology
830:microvilli
776:See also:
303:hyperballs
2676:Space.com
2582:205983729
2322:1537-5323
1763:6,000,000
1757:1,000,000
1537:(6 faces)
1525:Area of a
1433:≈
1289:≈
1182:≈
1064:≈
930:wildfires
842:organisms
725:does not
671:−
533:−
457:Γ
438:π
429:−
359:Γ
340:π
248:π
193:π
81:diffusion
56:) is the
2770:Archived
2741:Archived
2716:cite web
2627:16796576
2574:29592141
2529:11954818
2338:23434720
2330:23448890
2225:28572410
2217:19895606
2175:19505655
2167:18645354
2078:29843923
2029:32628526
1973:55488270
1919:55488270
1873:Specific
1865:18070616
1838:10697247
1781:See also
1738:50Ă—50Ă—50
1710:20Ă—20Ă—20
1682:12Ă—12Ă—12
1546:Ratio of
1530:6 Ă— side
1505:4.83598
908:such as
863:such as
854:behavior
571:prefixed
305:, where
60:between
2607:Bibcode
2509:Bibcode
2392:556–582
2069:6150810
1953:Bibcode
1899:Bibcode
1741:125,000
1732:6Ă—50Ă—50
1704:6Ă—20Ă—20
1676:6Ă—12Ă—12
1533:Area of
1517:Side of
1474:radius
1319:Capsule
991:length
955:Mercury
846:biology
813:Biology
796:compact
746:removed
731:sources
697:shape.
695:compact
2804:Ratios
2625:
2580:
2572:
2564:
2527:
2475:
2448:
2423:
2398:
2336:
2328:
2320:
2258:
2248:
2223:
2215:
2173:
2165:
2076:
2066:
2027:
1971:
1924:9 July
1917:
1863:
1853:
1836:
1826:
1735:15,000
1543:Volume
1463:Sphere
1457:5.148
1366:5.251
1069:14.697
986:Image
983:Shape
876:oxygen
792:porous
788:volume
659:
633:
611:
298:-balls
168:volume
164:sphere
160:sphere
93:oxygen
66:volume
54:sa/vol
32:times.
2701:(PDF)
2694:(PDF)
2578:S2CID
2562:JSTOR
2525:S2CID
2360:. In
2334:S2CID
2221:S2CID
2171:S2CID
1969:S2CID
1915:S2CID
1773:3:500
1751:1,000
1729:2,500
1726:50Ă—50
1713:8,000
1707:2,400
1698:20Ă—20
1685:1,728
1670:12Ă—12
1654:8Ă—8Ă—8
1648:6Ă—8Ă—8
1626:6Ă—6Ă—6
1620:6Ă—6Ă—6
1598:4Ă—4Ă—4
1592:6Ă—4Ă—4
1570:2Ă—2Ă—2
1564:6Ă—2Ă—2
1438:3.970
1383:edge
1313:5.31
1294:2.694
1223:edge
1206:5.72
1187:7.348
1153:edge
1105:edge
1088:7.21
1035:edge
968:Earth
964:Venus
943:Vesta
865:krill
838:cells
822:Cells
567:units
150:is a
101:water
58:ratio
52:, or
2722:link
2623:PMID
2570:PMID
2486:2010
2473:ISBN
2446:ISBN
2421:ISBN
2396:ISBN
2326:PMID
2318:ISSN
2285:(2).
2256:ISBN
2246:ISBN
2213:PMID
2163:PMID
2074:PMID
2025:PMID
1926:2021
1861:OCLC
1851:ISBN
1834:OCLC
1824:ISBN
1745:3:25
1717:3:10
1540:Side
1522:Side
1519:cube
1094:Cube
966:and
959:Mars
957:and
951:moon
916:and
872:lung
852:and
840:and
729:any
727:cite
597:SA:V
578:cube
284:For
217:and
147:ball
116:ball
95:and
83:and
64:and
50:SA/V
46:SA:V
36:The
2615:doi
2554:doi
2550:156
2517:doi
2310:doi
2306:181
2205:doi
2153:doi
2120:doi
2064:PMC
2056:doi
2015:doi
1961:doi
1907:doi
1701:400
1689:3:6
1679:864
1673:144
1661:3:4
1657:512
1651:384
1642:8Ă—8
1633:3:3
1629:216
1623:216
1614:6Ă—6
1605:3:2
1586:4Ă—4
1577:3:1
1558:2Ă—2
947:did
786:to
740:by
301:or
144:or
87:by
73:and
40:or
2785::
2718:}}
2714:{{
2673:.
2644:.
2621:.
2613:.
2601:.
2576:.
2568:.
2560:.
2548:.
2523:.
2515:.
2505:30
2503:.
2394:.
2364:,
2332:.
2324:.
2316:.
2304:.
2300:.
2283:46
2281:.
2277:.
2254:.
2219:.
2211:.
2201:85
2199:.
2195:.
2183:^
2169:.
2161:.
2149:54
2147:.
2143:.
2114:.
2110:.
2072:.
2062:.
2052:26
2050:.
2046:.
2023:.
2011:44
2009:.
2005:.
1967:.
1959:.
1949:29
1947:.
1943:.
1913:.
1905:.
1895:29
1893:.
1889:.
1859:.
1832:.
1723:50
1695:20
1667:12
1645:64
1617:36
1601:64
1595:96
1589:16
1567:24
1396:12
1342:12
1264:15
1247:10
1241:25
1236:12
1136:6
953:,
920:.
912:,
897:.
809:.
665:cm
639:cm
617:cm
582:cm
138:A
48:,
2724:)
2710:.
2659:.
2629:.
2617::
2609::
2603:9
2584:.
2556::
2531:.
2519::
2511::
2488:.
2454:.
2429:.
2404:.
2340:.
2312::
2262:.
2227:.
2207::
2177:.
2155::
2128:.
2122::
2116:9
2080:.
2058::
2031:.
2017::
1975:.
1963::
1955::
1928:.
1909::
1901::
1867:.
1840:.
1639:8
1611:6
1583:4
1573:8
1561:4
1555:2
1489:a
1486:3
1441:a
1427:a
1424:)
1419:5
1414:+
1411:3
1408:(
1401:3
1349:a
1346:5
1297:a
1283:a
1280:)
1275:5
1270:7
1267:+
1261:(
1252:5
1244:+
1190:a
1177:a
1171:6
1166:3
1120:a
1117:6
1072:a
1059:a
1053:6
1048:6
999:a
832:.
767:)
761:(
756:)
752:(
748:.
734:.
688:.
674:1
656:6
653:=
645:3
630:1
623:2
608:6
602:=
536:1
529:r
525:n
522:=
519:V
515:/
511:A
508:S
482:)
478:2
474:/
470:n
466:+
463:1
460:(
450:2
446:/
442:n
432:1
426:n
422:r
418:n
412:=
409:A
406:S
382:)
379:2
375:/
371:n
368:+
365:1
362:(
352:2
348:/
344:n
334:n
330:r
323:=
320:V
307:n
296:n
286:n
278:r
274:r
257:3
253:r
245:)
242:3
238:/
234:4
231:(
228:=
225:V
202:2
198:r
190:4
187:=
184:A
181:S
29:V
25:A
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
