Question

The curved surface area of the cylinder is $1760c{m}^2$ and its volume is $12320c{m}^3.$ Find its height.

Answer 1

Let r be the radius of the cylinder

and h be the height of the cylinder.

Given curved surface area of cylinder = $1760c{m}^2$

$2\pi rh=1760$

$\Rightarrow r=\frac{1760}{2rh}$ -----(1)

and volume of the cylinder = 12320$c{m}^2$

$\Rightarrow \pi r^{2}h$ = 12320

$\Rightarrow \pi (\frac{1760}{2\pi h}{)}^{2}h=12320$

$\Rightarrow \pi \left(\frac{(1760{)}^2}{A{\pi }^2{h}^2}\right)\times h=12320$

$\Rightarrow \frac{(1760{)}^2}{4\pi h}=12320$

$\Rightarrow h=\frac{(1760{)}^2}{4\pi \left(12320\right)}$

$\Rightarrow h=\frac{1760}{28\pi }$

$\Rightarrow h=\frac{1760\times 7}{88\times 22}$ [using $\pi =\frac{22}{7}]$

$\Rightarrow$ h=20 cm.

Hence height of cylinder =20 cm