Question

Volume and curved surface of a cylinder are 24750 $c{m}^3$ and 3300 $c{m}^2$ respectively. Find the height and radius of the base of cylinder.

Answer 1

Curved surface area $=3300c{m}^3$

volume $=24750c{m}^3$

CSA $=2\pi rh$

Let the height be h and radius be $r$

Also, $3300=2\pi \times r\times h$

$h=\frac{3300}{2\pi r}$ __ (1)

Also,

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

$24750=\pi \times r^2\times \frac{3300}{2\pi r}$

$24750=\frac{3300\times r}{2}$

$24750=1650\times r$

$r=\frac{24750}{1650}$

Radius $=15cm$

CSA = $2\pi rh$

$3300=2\pi \times 15\times h$

$h=\frac{3300}{2\pi \times 15}$

$h=35cm$

height $=35cm$