Question

The curved surface area of a cylindrical pillar is $264m^2$ and its volume is $924m^3$ . Find the diameter and the height of the pillar.

Answer 1

Find the dimension of the cylindrical pillar:

Let, $r,h$ be the radius and height of the pillar.

Given that, curved surface area and volume of pillar is $264m^{2}and924m^3$ respectively.

Curved surface area of cylinder of radius $r$ and height $h$ $=2\mathrm{\pi rh}$

$\therefore 2\mathrm{\pi rh}=264{\mathrm{m}}^2$

$$\begin{gathered} \Rightarrow rh=\frac{264}{2\mathrm{\pi }} \\ \Rightarrow rh=42m^2........\left(i\right) \end{gathered}$$

Volume of cylinder of radius $r$ and height $h$ $={\mathrm{\pi r}}^2\mathrm{h}$

$$\begin{gathered} \therefore {\mathrm{\pi r}}^2\mathrm{h}=924{\mathrm{m}}^3 \\ \Rightarrow {\mathrm{r}}^2\mathrm{h}=\frac{924{\mathrm{m}}^3}{\mathrm{\pi }} \\ \Rightarrow \mathrm{r}\left(\mathrm{rh}\right)=294{\mathrm{m}}^3 \\ \Rightarrow \mathrm{r}=\frac{294{\mathrm{m}}^3}{42{\mathrm{m}}^2} \\ \Rightarrow \mathrm{r}=7\mathrm{m} \end{gathered}$$

Substitute the value of radius in equation $\left(i\right)$

$h=\frac{42}{7}=6m$

Therefore, the diameter and height of the pillar is $14mand6m$ respectively.