Question

A sphere and a right cylinder have the same radius and volume. Find the radius r in terms of the height h of the cylinder.

Answer 1

Step 1:

Given

Volume of sphere = Volume of cylinder

Radius of sphere = Radius of cylinder = r (say)

Step 2:

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

$\frac{3}{4}h=r$

Hence the r in terms of h is $\frac{3}{4}$h.