Question

A solid sphere of radius $r$ is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is $4cm$, its height $24cm$ and thickness $2cm$, find the value of $r$.

Answer 1

Volume of solid sphere=volume of hollow cylinder

$\Rightarrow \frac{4}{3}\pi r^3=\pi (r_2^2-r_1^2)\times h\Rightarrow \frac{4}{3}\times r^3=({\left(4\right)}^2-{\left(2\right)}^2)\times 24[\because r_2=4,w=2㎝;\therefore r_1=4-2=2㎝]$

$\Rightarrow r^3=\frac{12\times 24\times 3}{4}=216\Rightarrow r=\sqrt[3]{3216}=6cm$