Question

The curved surface area and volume of a pillar are 264 m² and 396 m³, respectively. Find the diameter and height of the pillar.

Answer 1

Curved surface area of the pillar = 264 m²
Volume of the pillar = 396 m³
Dividing the curved surface area of the pillar by its volume, we get:
$$\begin{gathered} \Rightarrow \frac{2\mathrm{\pi }rh}{\mathrm{\pi }{r}^{2}h}=\frac{264}{396} \\ \Rightarrow \frac{2}{r}=\frac{264}{396} \\ \Rightarrow r=\frac{396}{264}\times 2 \\ \Rightarrow r=3\mathrm{m} \end{gathered}$$
Diameter = 2r = 6 m
So, diameter of the pillar is 6 m.
Curved surface area = 264 m²
$$\begin{gathered} \Rightarrow 2\mathrm{\pi }rh=264 \\ \Rightarrow h=\frac{264}{2\mathrm{\pi }r} \\ \Rightarrow h=\frac{264\times 7}{2\times 22\times 3} \\ \Rightarrow h=14\mathrm{m} \end{gathered}$$
Height of the pillar is 14 m.