<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 (
<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 (
what has more surface area cube or sphere
what has more surface area cube or sphere
Cube
Cube