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 diameter of the third ball.

Answer 1

Let $r$ be the radius of the third ball. Then,

Volume of spherical ball of radius $3cm=$ Volume of three small ball of radius $(1.5cm,2cm,rcm$)

$\Rightarrow \frac{4}{3}\pi \times 3^3=\frac{4}{3}\pi \times {\left(1.5\right)}^3+\frac{4}{3}\pi \times 2^3+\frac{4}{3}\pi r^3$

$\Rightarrow 27=\frac{27}{8}+8+r^3$ [on canceling $\frac{4\pi }{3}$ from both sides]

$\Rightarrow r^3=27-8-\frac{27}{8}=\frac{125}{8}$

$\Rightarrow r=\sqrt[3]{3\frac{5^3}{2^3}}=\frac{5}{2}$ $=2.5cm$

Hence, the diameter of the third ball is $2\times 2.5=5cm$.