Question

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

Answer 1

Step 1. Find the radius of the cylinder.

Given that, the circumference of the base $=110cm$

Circumference of the base of the cylinder of radius $r$ $=2\mathrm{\pi r}$

$\therefore 110=2\mathrm{\pi r}$

$\Rightarrow 110=2\times \frac{22}{7}\times r$ $(\mathrm{\pi }=\frac{22}{7})$

$\Rightarrow r=\frac{110\times 7}{22\times 2}$

$\Rightarrow r=\frac{35}{2}cm$

Step 2: Find the height of the cylinder.

We have, curved surface area (C.S.A.) of the cylinder $=4400sq.cm$

The curved surface area of the cylinder of height $h$ and radius $r$ $=2\mathrm{\pi rh}$

$\therefore 2\mathrm{\pi rh}=4400$

$\Rightarrow 2\times \frac{22}{7}\times \frac{35}{2}\times h=4400$ $(\mathrm{\pi }=\frac{22}{7})$

$\Rightarrow 110\times h=4400$

$\Rightarrow h=\frac{4400}{110}$

$\Rightarrow h=40cm$

Hence, the height of the cylinder is $40cm$.