Question

A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

Answer 1

Let radius of spherical ball = r

Then radius of smaller spherical ball `=r/4`

Let n be the no. of balls made by big spherical ball.

Clearly,

Volume of big spherical balls = n × volume of one smaller ball

`4/3 pir^3 = n xx 4/3 pi (r / 4)^3`

      `r^3 = n xx r^3/64`

        ` n = 64`

Hence, the no. of balls = 64.