Question

A metallic sphere of radius $4.2cm$ is melted and recast into the shape of a cylinder of radius $7cm$. Find the height of the cylinder (in cm).

Answer 1

Volume of sphere is equal to the volume of cylinder because mass and density does not change.

$V_1=V_2$

$\frac{4}{3}\pi r^3=\pi R^{2}H$

$H=\frac{4r^3}{3R^2}$

$H=\frac{4\times {4.2}^3}{3\times 7^2}$

$H\approx 2cm$