the surface area of a sphere and cube are equal. prove that their volumes are in the ratio 1: 6^1/2
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the surface area of a sphere and cube are equal. prove that their volumes are in the ratio 1: 6^1/2
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i.e. 4 πr2 = 6a2
so, a2 = 4πr2 / 6 .......(2)
a = 2r root π / 6 ......(1)
now, volume of sphere = 4/3 πr3
volume of cube = a3
that means , volume of cube = a2 X a
a2 X a = 4 πr2 X 2r root π / 6
= 4/3 πr3 X root π/6
therefore, r3 : a3 = 4/3π r3 : 4/3 π r3 X root π / 6
thus, r3 : a3 = 1 : root π / 6
hope it is right..