Question

A spherical iron ball of radius 9 cm is melted and recast into three spherical balls. If the radius of two balls be 1 cm and 8 cm, find the radius (in cm) of the third ball.

Answer 1

Given that, a spherical ball of radius $9cm$ is melted and recast into three spherical balls.

The radius of two balls is $1cm$ and $8cm$ respectively.

To find out: Radius of the third ball.

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

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

So, volume of the original sphere $=\frac{4}{3}\pi \times 9^3$

Volume of the original ball $=$ Total volume of the three balls.

$\therefore \frac{4}{3}\pi \times 9^3=\frac{4}{3}\pi \times 1^3+\frac{8}{3}\pi \times 8^3+\frac{4}{3}\pi r^3$

Dividing both sides by $\frac{4}{3}\pi$, we get:

$\Rightarrow 9^3=1^3+8^3+r^3$

$\Rightarrow r^3=9^3-8^3-1^3$

$\Rightarrow r^3=729-512-1$

$\Rightarrow r^3=216$

$\Rightarrow r=6cm$

Thus, the radius of the third ball is $6cm$.