Question

the surface area of a sphere and cube are equal. prove that their volumes are in the ratio 1: 6^1/2

Answer 1

according to the question, these both are equal...!!

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..

Answer 2

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