Question

The curved surface area pf a cylinder is $440c{m}^2$ and the circumference of its base is $110cm$. Find the height and the volume of the cylinder.

Answer 1

Consider $r$ as the radius as $h$ as the height of cylinder

It is given that

Surface area of cylinder $=2\pi rh$

By substituting the values

$2\pi rh=4400....\left(1\right)$

It is given that circumferences of its base $=2\pi rh$

So we get

$2\pi rh=110$

We know that

$\frac{2\pi rh}{2\pi r}=\frac{4400}{110}$

On further calculation

$h=40cm$

Substituting the value of $h$ in $\left(1\right)$

We get

$2\times \frac{22}{7}\times r\times 40=4400$

On further calculation $r=\frac{4400\times 7}{44\times 40}$

So we get

$r=17.5cm$

We know that

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

By substituting the values

Volume of cylinder $=\frac{22}{7}\times (17.5{)}^2\times 40$

So we get

Volume of cylinder $=38500c{m}^3$

Therefore, the height of the cylinder is $40cm$ and the volume is $38500c{m}^3$.