Question

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Answer 1

Radius of sphere = 4.2 cm, radius of cylinder = 6 cm
Volume of sphere
$=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\pi \times {4.2}^3$
Volume of cylinder
$=\pi r^{2}h$
$=\pi \times 6^2\times h$
Since volume of cylinder =volume of sphere
$\pi \times 6^2\times h=\frac{4}{3}\pi \times {4.2}^3$
Hence, height of cylinder
$h=\frac{4\times \pi \times {4.2}^3}{3\times \pi \times 6^2}$
$=2.744cm$