(Q2).Surface area of a sphere and cube are equal. Then find the ratio of their volumes.

Let a cube with side ‘a’.

Then its surface area = 6a2

By problem, surface area of the sphere = 4πr2

Surface area of the cube = 6a2

∴ 4πr2 = 6a2⇒ r2=
a 2
π
⇒ r = √(
a2
π
 ) = √(
π
 )a

Volume of the cube V = a3

Volume of the sphere V =
4
3
 πr3
=
. π .(√
π
 .a × √
π
 .a × √
π
 .a )
=
. π .
√
π√π
 a3
=
√
√π
 a3
=
√
√
 a3
Ratio of the volumes =
√
√
 a3: a3

=√:√