Question

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. The height of the pillar is
(a) 4 m
(b) 5 m
(c) 6 m
(d) 7 m

Answer 1

(c) 6 m

Curved surface area = 264 m²
Volume = 924 m³
Let r m be the radius and h m be the height of the cylinder.
Then we have:
$$\begin{gathered} 2\mathrm{\pi }rh=264\mathrm{and}\mathrm{\pi }{r}^{\mathit{2}}h=924 \\ \Rightarrow rh\mathit{}=\frac{264}{2\mathrm{\pi }} \\ \Rightarrow h\mathit{}=\frac{264}{2r\times \mathrm{\pi }} \\ \mathrm{Now},\mathrm{\pi }{r}^{\mathit{2}}h=\mathrm{\pi }\times r^{\mathit{2}}\times \frac{264}{2r\times \mathrm{\pi }}=924 \\ \Rightarrow r=\frac{924\times 2}{264} \\ \Rightarrow r=7\mathrm{m} \\ \therefore h\mathit{}=\frac{264\times 7}{2\times 7\times 22}=6\mathrm{m} \end{gathered}$$