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
Solution:
(c) 6 m
The curved surface area of a cylindrical pillar
$=2 \pi r h$
Therefore, $2 \pi r h=264$
Volume of a cylinder $=\pi r^{2} h$
Therefore, $\pi r^{2} h=924$
Hence,
$\frac{\pi r^{2} h}{2 \pi r h}=\frac{924}{264}$
$\Rightarrow \frac{r}{2}=\frac{924}{264}$
$\Rightarrow r=\left(\frac{924 \times 2}{264}\right)$
$\Rightarrow r=7 \mathrm{~m}$
Therefore,
$2 \pi r h=264$
$\Rightarrow 2 \times \frac{22}{7} \times 7 \times h=264$
$\Rightarrow h=\frac{264}{44}$
$\Rightarrow h=6 \mathrm{~m}$
Hence, the height of the pillar is 6 m.