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?
Solution:
Let radius of spherical ball = r
Then radius of smaller spherical ball $=\frac{r}{4}$
Let n be the no. of balls made by big spherical ball.
Clearly,
Volume of big spherical balls = n × volume of one smaller ball
$r^{3}=n \times \frac{r^{3}}{64}$
$n=64$
Hence, the no. of balls = 64