The surface area to volume ratio of shapes

For two masses the same, the volumes will also be equal. Let the volume = 1000 units (chosen for convenience)

Sphere volume 4/3πr3 = 1000

r3 = 1000 x 3/ 4π

r3 = 1000 x 3π/4 = 238.73

r = 3√ 238.73 = 6.203

Surface area of this sphere = 4πr2 = 4 x π x 6.203 x 6.203 = 483.6

Therefore surface area to volume ratio for sphere = 483.6/1000 = 0.484 (3 sig figs)

Cube volume = d3 = 1000

Cube side 'd' = 10

Surface area = 6 x d2 = 600

Therefore surface area to volume ratio for cube = 600/1000 = 0.600 (3 sig figs)