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 S_{s} be the surface area of sphere and S_{c} be the surface area of cube and V_{s} be volume of sphere and V_{c} be volume of cube

∴ S_{s} = 4πr^{2} and S_{c} = 4a^{2}

Given that surface area of sphere and cube are equal

∴ S_{s} = S_{c}

4πr^{2} = 6a^{2}

r^{2}/ a^{2} = 3/2π

V_{s} = (4/3) πr^{3}

V_{c} = a^{3}

∴ V_{s}/V_{c} = 4πr^{3}/3a^{3}

Using (i)

∴ V_{s}/V_{c} = √21/√11

Therefore ratio of their volumes is V_{s}:V_{c} = √21:√11

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