Question

A spherical metallic ball of radius $3cm$ is melted and recast into three spherical balls. The radii of two of these balls are $2\cdot 5cm$ and $2cm$ respectively. Find the radius of the third ball.

Answer 1

When a solid is converted from one form to another, the amount of volume remains the same.

Volume of Bigger Sphere = Sum of Volumes of Smaller spheres.

Formula for volume of a sphere of radius $r$ $V=\frac{4}{3}\pi r^3$

$\frac{4}{3}\pi (3{)}^3=\frac{4}{3}\pi (2.5{)}^3+\frac{4}{3}\pi (2{)}^3+\frac{4}{3}\pi (x{)}^3$

$27=15.625+8+x^3$

$x^3=3.375$

$x=\sqrt[3]{33.375}$

$x=1.5cm$