<P> The surface to volume ratios of organisms of different sizes also leads to some biological rules such as Bergmann's rule and gigantothermy . </P> <P> In the context of wildfires, 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> <Table> <Tr> <Th> Shape </Th> <Th> </Th> <Th> Characteristic Length a (\ displaystyle a) </Th> <Th> Surface Area </Th> <Th> Volume </Th> <Th> SA / V ratio </Th> <Th> SA / V ratio for unit volume </Th> </Tr> <Tr> <Td> Tetrahedron </Td> <Td> </Td> <Td> side </Td> <Td> 3 a 2 (\ displaystyle (\ sqrt (3)) a ^ (2)) </Td> <Td> 2 a 3 12 (\ displaystyle (\ frac ((\ sqrt (2)) a ^ (3)) (12))) </Td> <Td> 6 6 a ≈ 14.697 a (\ displaystyle (\ frac (6 (\ sqrt (6))) (a)) \ approx (\ frac (14.697) (a))) </Td> <Td> 7.21 </Td> </Tr> <Tr> <Td> Cube </Td> <Td> </Td> <Td> side </Td> <Td> 6 a 2 (\ displaystyle 6a ^ (2)) </Td> <Td> a 3 (\ displaystyle a ^ (3)) </Td> <Td> 6 a (\ displaystyle (\ frac (6) (a))) </Td> <Td> 6 </Td> </Tr> <Tr> <Td> Octahedron </Td> <Td> </Td> <Td> side </Td> <Td> 2 3 a 2 (\ displaystyle 2 (\ sqrt (3)) a ^ (2)) </Td> <Td> 1 3 2 a 3 (\ displaystyle (\ frac (1) (3)) (\ sqrt (2)) a ^ (3)) </Td> <Td> 3 6 a ≈ 7.348 a (\ displaystyle (\ frac (3 (\ sqrt (6))) (a)) \ approx (\ frac (7.348) (a))) </Td> <Td> 5.72 </Td> </Tr> <Tr> <Td> Dodecahedron </Td> <Td> </Td> <Td> side </Td> <Td> 3 25 + 10 5 a 2 (\ displaystyle 3 (\ sqrt (25 + 10 (\ sqrt (5)))) a ^ (2)) </Td> <Td> 1 4 (15 + 7 5) a 3 (\ displaystyle (\ frac (1) (4)) (15 + 7 (\ sqrt (5))) a ^ (3)) </Td> <Td> 12 25 + 10 5 (15 + 7 5) a ≈ 2.694 a (\ displaystyle (\ frac (12 (\ sqrt (25 + 10 (\ sqrt (5))))) ((15 + 7 (\ sqrt (5))) a)) \ approx (\ frac (2.694) (a))) </Td> <Td> 5.31 </Td> </Tr> <Tr> <Td> Capsule </Td> <Td> </Td> <Td> radius (R) </Td> <Td> 4 π a 2 + 2 π a ∗ 2 a = 8 π a 2 (\ displaystyle 4 \ pi a ^ (2) + 2 \ pi a * 2a = 8 \ pi a ^ (2)) </Td> <Td> 4 π a 3 3 + π a 2 ∗ 2 a = 10 π a 3 3 (\ displaystyle (\ frac (4 \ pi a ^ (3)) (3)) + \ pi a ^ (2) * 2a = (\ frac (10 \ pi a ^ (3)) (3))) </Td> <Td> 12 5 a (\ displaystyle (\ frac (12) (5a))) </Td> <Td> 5.251 </Td> </Tr> <Tr> <Td> Icosahedron </Td> <Td> </Td> <Td> side </Td> <Td> 5 3 a 2 (\ displaystyle 5 (\ sqrt (3)) a ^ (2)) </Td> <Td> 5 12 (3 + 5) a 3 (\ displaystyle (\ frac (5) (12)) (3 + (\ sqrt (5))) a ^ (3)) </Td> <Td> 12 3 (3 + 5) a ≈ 3.970 a (\ displaystyle (\ frac (12 (\ sqrt (3))) ((3 + (\ sqrt (5))) a)) \ approx (\ frac (3.970) (a))) </Td> <Td> 5.148 </Td> </Tr> <Tr> <Td> Sphere </Td> <Td> </Td> <Td> radius </Td> <Td> 4 π a 2 (\ displaystyle 4 \ pi a ^ (2)) </Td> <Td> 4 π a 3 3 (\ displaystyle (\ frac (4 \ pi a ^ (3)) (3))) </Td> <Td> 3 a (\ displaystyle (\ frac (3) (a))) </Td> <Td> 4.836 </Td> </Tr> </Table> <Tr> <Th> Shape </Th> <Th> </Th> <Th> Characteristic Length a (\ displaystyle a) </Th> <Th> Surface Area </Th> <Th> Volume </Th> <Th> SA / V ratio </Th> <Th> SA / V ratio for unit volume </Th> </Tr>

What has more surface area cube or sphere