Question

The total surface area of a solid cylinder is $616$ $c{m}^2$. If the ratio between its curved surface area and total surface area is $1:2$; find the volume of the cylinder.

• A. $1078$ cu. cm
• B. $1070$ cu.cm
• C. $1700$$ cu.cm
• D. $1087$ cu. cm

Answer 1

The correct option is A $1078$ cu. cm

Given, total surface area of cylinder $616c{m}^2$
$\therefore 2\pi r(r+h)=616$............(1)
$\frac{curvedsurfacearea}{totalsurfacearea}=\frac{1}{2}$
$\therefore \frac{2\pi rh}{2\pi r(r+h)}=\frac{h}{r+h}=\frac{1}{2}$
$\therefore 2h=r+h,r=h$
Substituting this value in equation (1), we get
$2\pi r2r=616$
$\therefore 4r^2\pi =616$
$\therefore r=7,h=7$
$\therefore$ volume of the cylinder $=\pi \left(7^2\right)\left(7\right)=1078c{m}^3=1078cu.cm$.