Question

The ration between the curved surface and total surface of a cylinder is 1:2.Find the volume of the cylinder given that its total surface area is 616$c{m}^2$

Answer 1

Solution :-

Given $\frac{2\pi rh}{2\pi rh+2\pi r^2}=\frac{1}{2}$

$\Rightarrow 4\pi rh=2\pi rh+2\pi r^2$

$\Rightarrow 2\pi rh=2\pi r^2$

$\Rightarrow h=r$

Now, Total surface area = $616c{m}^2$

$2\pi r\times r+2\pi r^2=616$

$2\pi r^2+2\pi r^2=616$

$\Rightarrow 4\pi r^2=616$

$\Rightarrow r^2=\frac{616\times 7}{4\times 22}=\frac{4.312}{88}=49$

$\Rightarrow r=\pm 7cm$

$r=7cm$

Volume of cylinder = $\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 7$

$=1.078c{m}^3$