Question

A solid sphere of radius $6cm$ is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is $5$ cm and its height is $32$ cm, then find the thickness of the cylinder.

Answer 1

Volume of sphere = Volume of hollow cylinder
$\left(\frac{4}{3}\right)\pi r^3=\pi h(R^2-r^2)$
$\left(\frac{4}{3}\right)6^3=32(5^2-r^2)$
$25-r^2=\left[\right(\frac{4}{3}\left)216\right]/32$
$25-r^2=\left[\right(4\left)72\right]/32$
$25-r^2=9$
$r^2=25-9=16$
$r=4$
Thickness $R-r$
$=5-4$
$=1cm$