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

Hint- In order to solve this question we will use the formula for volume of sphere i.e. $\dfrac{4}{3}\pi {r^3}$ because here spherical ball is considered as a sphere. And we know that when one shape is melted into another shape their volume remains the same.

Complete step-by-step answer:
In order to find the number of balls that can be made from the original spherical iron ball, we have given that a spherical ball of iron has been melted and made into smaller balls and the radius of each smaller ball is one-fourth of the radius of the original one.
Let the radius of the smaller ball be $r$ .
And we know that
The radius of each smaller ball is one-fourth of the radius of the original one.
$r = \dfrac{1}{4} \times $ radius of original ball
Or Radius of original ball $ = 4r$
And we know that the volume of sphere $ = \dfrac{4}{3}\pi {r^3}$
Volume of original ball $ = \dfrac{4}{3}\pi {\left( {4r} \right)^3}$
And volume of smaller ball $ = \dfrac{4}{3}\pi {r^3}$
Number of balls= volume of original ball $ \div $ volume of smaller ball
$
   = \dfrac{{ = \dfrac{4}{3}\pi {{\left( {4r} \right)}^3}}}{{ = \dfrac{4}{3}\pi {{\left( r \right)}^3}}} \\
   = \dfrac{{64{r^3}}}{{{r^3}}} \\
   = 64 \\
 $
Thus, number of balls made=64

Note- whenever we face such types of questions the key concept is that we should write what is given to us then then convert the statements into equations like we did. Then we apply the formula for volume of sphere for original ball and smaller ball and then we divide them to get the number of required balls.