Question:
The lateral surface area of a cylinder of length 14 m is 220 m2. Find the volume of the cylinder.
Solution:
Length $=$ height $=14 \mathrm{~m}$
Lateral surface area $=2 \pi \mathrm{rh}=220 \mathrm{~m}^{2}$
Radius $=r=\frac{220}{2 \pi \mathrm{h}}=\frac{220 \times 7}{2 \times 22 \times 14}=\frac{10}{4}=2.5 \mathrm{~m}$
$\therefore$ Volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\frac{22}{7} \times 2.5 \times 2.5 \times 14=275 \mathrm{~m}^{3}$