Question

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

Answer 1

Given that, 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 $2cm$.

To find out: The radius of the third ball.

Let the radius of the third ball be $rcm$

Here, volume of the original spherical ball $=$ sum of the volumes of all the three smaller spherical balls

We know that, volume of a sphere is $\frac{4}{3}\pi r^3$

$\therefore \frac{4}{3}\pi (3{)}^3=\frac{4}{3}\pi (1.5{)}^3+\frac{4}{3}\pi (2{)}^3+\frac{4}{3}\pi r^3$

$\Rightarrow 3^3=(1.5{)}^3+(2{)}^3+r^3$

$\Rightarrow r^3=27-3.375-8=15.625$

$\Rightarrow r=2.5$.

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