Question:
The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110 cm. Find the volume of the cylinder.
Solution:
Curved surface area $=2 \pi r h=4400 \mathrm{~cm}^{2}$
Circumference $=2 \pi \mathrm{r}=110 \mathrm{~cm}$
Now, height $=h=\frac{\text { curved surface area }}{\text { circumference }}=\frac{4400}{110}=40 \mathrm{~cm}$
Also, radius, $r=\frac{4400}{2 \pi \mathrm{h}}=\frac{4400 \times 7}{2 \times 22 \times 40}=\frac{35}{2}$
$\therefore$ Volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} \times 40=22 \times 5 \times 35 \times 10=38500 \mathrm{~cm}^{3}$