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:

Radius of sphere $=4.2cm$

Radius of cylinder $=6cm$

Also given that the object formed by recasting the sphere will be the same in volume.

So, Volume of Sphere $=$ Volume of Cylinder.

$$\begin{gathered} \left(\frac{4}{3}\right)\pi r^3=\pi r^{2}h \\ \left(\frac{4}{3}\right)\pi {\left(4.2\right)}^3=\pi {\left(6\right)}^{2}h \\ h=\frac{4\times {\left(4.2\right)}^3}{3\times 12}={\left(1.4\right)}^3 \end{gathered}$$

h $={\left(1.4\right)}^3=2.744cm$

Hence, the height of the cylinder is $2.744cm$.