Question

A spherical ball of radius $3cm$ is melted and recast into three spherical balls. The radii of two of the balls are $1.5cm$ and $2cm.$ Find the radius of the third ball.

Answer 1

Let the radius of the third ball be $x.$

Given:

$R=3cm$

$r_1=1.5cm$

$r_2=2cm$

$r_3=x$

The volume of the sphere with radius $3$ will be equal to the sum of the volume of the three spheres formed. Hence,

$\begin{array}{cc}\frac{4}{3}\pi R^3& =\frac{4}{3}\pi {r_1}^3+\frac{4}{3}\pi {r_2}^3+\frac{4}{3}\pi {r_3}^3\\ {\left(3\right)}^3& ={\left(1.5\right)}^3+{\left(2\right)}^3+x^3\\ 27& =3.375+8+x^3\\ x^3+11.375& =27\\ x^3& =15.625\\ x& =2.5cm\end{array}$

Hence, the radius of the third ball is equal to $2.5cm.$