Question

A metallic sphere of radius $15cm$ is melted and recast into the shape of a cylinder of radius $15cm$. Find the height of the cylinder.

Answer 1

The radius of Metallic sphere is $15cm$

The volume of sphere $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \pi \times 15\times 15\times 15$

$=4500\pi$ $c{m}^3$

The volume of sphere is same as volume of cylinder. Let $h$ be the height of the cylinder.

Volume of cylinder$=\pi \times r^2\times h$

$\pi \times 15\times 15\times h$

$225\pi hc{m}^3$

According to the given condition,

$225\pi h=4500\pi$

Thus, $h=20cm$

So the height of the cylinder is $20cm$