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

Given

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

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

Find out

We have to find the height of the cylinder

Solution

let the height of the cylinder $=h$

The volume of cylinder $=$ Volume of a sphere

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

Answer

Therefore, the height of the cylinder $=2.74cm$