Question:
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and height of the pillar.
Solution:
Curved surface area $=2 \pi \mathrm{rh}=264 \mathrm{~m}^{2}$
$\therefore r=\frac{264}{2 \pi \mathrm{h}}=\frac{132}{\pi \mathrm{h}} m$
Volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\pi \times \frac{132}{\pi \mathrm{h}} \times \frac{132}{\pi \mathrm{h}} \times \mathrm{h}=924 \mathrm{~m}^{3}$
$\therefore h=\frac{132 \times 132 \times 7}{22 \times 924}=6 \mathrm{~m}$
Now, $r=\frac{132}{\pi \mathrm{h}}=\frac{132 \times 7}{22 \times 6}=7 m$
i.e., diameter of the pillar, $d=7 \times 2=14 \mathrm{~m}$