Question

A copper sphere of radius $3cm$ is melted and recast into a right circular cone of height $3cm$. Find the radius of the base of the cone,

Answer 1

Copper sphere radius $r=3cm$

Cone height $h=3cm$

Radius of the base of cone $=R=(?)$

$\to$ Volume of copper sphere $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \pi \times (3{)}^3$

$=36\pi c{m}^3$

$\to$ Volume of Cone $=\frac{1}{3}\pi R^2.h$

$=\frac{1}{3}\times \pi \times R^2\times 3$

$=\pi R^{2}c{m}^3$

$\to$ Volume of copper sphere = Volume of cone

$\therefore 36\pi =\pi R^2$

$\therefore R^2=36$

$\therefore R=6cm$