Question

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

• A. $5$ cm
• B. $20$ cm
• C. $10$ cm
• D. $15$ cm

Answer 1

Answer: (B)

The correct option is D $20$ cm
Given, the curved surface area of the cylinder is $1760$ sq. cm and its volume is $12320$ cubic cm

Let the radius of the cylinder is $r$ and height is $h$

Then curved surface area $=$ $2\pi rh=1760$

$\Rightarrow r=\frac{880}{\pi h}$ .......(1)

The volume $=$ $\pi r^{2}h=12320$

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

From (1) and (2), we get

${\left[\frac{880}{\pi h}\right]}^2=\frac{12320}{\pi h}$

$\Rightarrow \frac{880}{\pi h}\times \frac{880}{\pi h}=\frac{12320}{\pi h}$

$\Rightarrow \frac{880\times 880}{\pi h}=12320$

$\Rightarrow 12320\pi h=774400$

$\Rightarrow h=\frac{774400\times 7}{12320\times 22}=20cm$