Q. 143.9( 10 Votes )

The surface areas of a sphere and a cube are equal. Find the ratio of their volumes. [Takes π = 22/7.]

Answer :

Let r be the radius of sphere and a be the side length of cube.

Let Ss be the surface area of sphere and Sc be the surface area of cube and Vs be volume of sphere and Vc be volume of cube

Ss = 4πr2 and Sc = 4a2

Given that surface area of sphere and cube are equal

Ss = Sc

4πr2 = 6a2

r2/ a2 = 3/2π

Vs = (4/3) πr3

Vc = a3

Vs/Vc = 4πr3/3a3

Using (i)

Vs/Vc = √21/√11

Therefore ratio of their volumes is Vs:Vc = √21:√11

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