Question

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

Answer 1

We have to find the height of the cylinder.

Given:

the radius of the sphere ($R$) $=4.2cm$

the radius of cylinder ($r$) $=6cm$

Solution

let the height of the cylinder be $h$

As given that the sphere is melted and recast into the shape of a cylinder.

So,Volume of cylinder $=$ Volume of sphere

$$\begin{gathered} \pi r^{2}h=\frac{4}{3}\pi R^3 \\ \pi {\left(6\right)}^{2}h=\frac{4}{3}\pi {(4.2)}^{3}36h=\frac{4}{3}(4.2\times 4.2\times 4.2) \\ h=1.4\times 1.4\times 1.4cm \\ h=2.74cm \end{gathered}$$

Hence, the height of the cylinder is $2.74cm$.