Question

A container in shape of a cylinder can store 7 litres of water. If the curved surface area of the cylinder is $1000c{m}^2$. What is the height of the cylinder?

• A. 14.266 cm
• B. 13.464 cm
• C. 11.363 cm
• D. 22. 336 cm

Answer 1

The correct option is C

11.363 cm

Given: Volume of the cylinder $=\pi r^{2}h=7litres=7000c{m}^3(\because 1litre=1000c{m}^3)$

Also, curved surface area of cylinder $=2\pi rh=1000c{m}^2$
Ratio of volume to curved surface area = $\frac{7000}{1000}=7$
$\Rightarrow$ $\frac{\pi r^{2}h}{2\pi rh}=7$
$\Rightarrow$ $\frac{r}{2}=7$
$\Rightarrow$ $r=14cm$

$\because$ Curved surface area of the cylinder = $1000c{m}^2$
$\Rightarrow$ $2\pi rh=1000c{m}^2$
$\Rightarrow$ $h=\frac{1000}{2\pi \times 14}$
$\Rightarrow$ $h=11.363cm$