Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is $1:2$. Find the volume of the cylinder, if its total surface area is 616 $c{m}^2$

Answer 1

Ratio of curved surface area and total surface area of a cylinder $=1:2$

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

$\therefore$ Curved surface area $=\frac{616\times 1}{2}$

$=308\times 1=308c{m}^2$

$\therefore 2\pi rh=308$

$\Rightarrow \frac{2\times 22}{7}rh=308$

$\Rightarrow rh=\frac{308\times 7}{2\times 22}=49$...(i)

Also, $2\pi r^2=616-308=308c{m}^2$

$\Rightarrow 2\times \frac{22}{7}{r}^2=308$

$\Rightarrow r^2=\frac{308\times 7}{2\times 22}=49=(7{)}^2$

$\therefore r=7cm$

and $h=\frac{49}{r}=\frac{49}{7}=7cm$ [From (i)]

Now volume = $\pi r^{2}h$

=$\frac{22}{7}\times 7\times 7\times 7=1078c{m}^3$