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

Step 1: Find equation for height of the pillar

Given, curved surface area of cylindrical pillar $=264{\mathrm{m}}^2$

We know that, curved surface area of cylinder $=2\mathrm{\pi rh}$ , where, $r$ is the radius of cylindrical pillar and $h$ is height

By the problem,

$$\begin{gathered} \Rightarrow 2\mathrm{\pi rh}=264 \\ \Rightarrow 2\times \frac{22}{7}\times r\times h=264 \\ \Rightarrow h=\frac{264\times 7}{2\times 22\times r} \\ \Rightarrow h=\frac{42}{r} \end{gathered}$$

Step 2: Find radius of the pillar

Given, volume of cylindrical pillar $=924m^3$

We know that volume of cylinder $={\mathrm{\pi r}}^2\mathrm{h}$

By the problem,

$$\begin{gathered} \Rightarrow {\mathrm{\pi r}}^2\mathrm{h}=924 \\ \Rightarrow \frac{22}{7}{r}^{2}h=924 \\ \Rightarrow r^2=\frac{924\times 7}{22\times h} \\ \Rightarrow r^2=\frac{924\times 7\times r}{22\times 42}\left[\because h=\frac{42}{r}\right] \\ \Rightarrow r=\frac{924\times 7}{22\times 42} \\ \Rightarrow r=7 \end{gathered}$$

$\therefore$ Radius of the cylindrical pillar $=7m$

Step 3: Find the diameter and the height of the pillar

$\therefore$ Diameter of the pillar $=2\times 7=14m$

$\therefore$ Height of the pillar $=\frac{42}{r}=\frac{42}{7}=6m$

Hence, the diameter and the height of the pillar is $14m$ and $6m$ respectively.