Question

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is

(a) 100 π

(b) 75 π

(c) 60 π

(d) 50 π

Answer 1

In the given problem, Let the radius of smaller spherical balls which can be made from a bigger ball be x units.

Here,

The radius of the bigger ball (r₁) = 10 cm

The radius of the smaller ball (r₂) = x cm

The number of smaller balls = 8

So, volume of the big ball is equal to the volume of 8 small balls.

Volume of the big balls = volume of the 8 small balls

Further, solving for x, we get,

Now, surface area of a small ball of radius 5 cm =

Therefore, the surface area of the small spherical ball is. So, the correct option is (a).