# The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110 cm.

Question:

The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110 cm. Find the height and the volume of the cylinder.

Solution:

Let r be the radius and h be the height of the cylinder.

Circumference of its base(circle) = 110 cm.

$\Rightarrow 2 \pi r=110 \Rightarrow r=\frac{110}{2 \pi} \Rightarrow r=\frac{110}{2 \times \frac{22}{7}} \Rightarrow r=\frac{110 \times 7}{2 \times 22} \Rightarrow r=\frac{35}{2} \mathrm{~cm}$

Curved surface area of a cylinder $=4400 \mathrm{~cm}^{2}$.

$\Rightarrow 2 \pi r h=4400 \Rightarrow h=\frac{4400}{2 \pi r} \Rightarrow h=\frac{4400}{2 \times \frac{22}{7} \times \frac{35}{2}}$

$\Rightarrow h=\frac{4400 \times 7 \times 2}{2 \times 22 \times 35} \Rightarrow h=40 \mathrm{~cm}$

Also, Volume of the cylinder $=\pi r^{2} h=\frac{22}{7} \times\left(\frac{35}{2}\right)^{2} \times 40=\frac{22 \times 35 \times 35 \times 40}{7 \times 2 \times 2}=38500 \mathrm{~cm}^{3} .$