The curved surface area of a cylinder is 1210 cm2 and its diameter is 20 cm.
Question:

The curved surface area of a cylinder is 1210 cm2 and its diameter is 20 cm. Find its height and volume.

Solution:

Curved surface area = 1210 cm2
Suppose that the height of cylinder is h cm.
We have r = 10 cm

Now, $1210=2 \pi r h$

$\Rightarrow 1210=2 \times \frac{22}{7} \times 10 \times h$

$\Rightarrow h=\frac{1210 \times 7}{2 \times 22 \times 10}=\frac{11 \times 7}{2 \times 2}=19.25 \mathrm{~cm}$

$\therefore$ Volume of the cylinder $=\pi r^{2} h$

$=\frac{22}{7} \times 10^{2} \times 19.25 \mathrm{~cm}^{3}$

$=2200 \times 2.75 \mathrm{~cm}^{3}=6050 \mathrm{~cm}^{3}$