The ratio between the curved surface area and the total surface area of a right circular cylinder is 1: 2. Find
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 $616 \mathrm{~cm}^{2}$.

Solution:

Let, r be the radius of cylinder

h be the radius of cylinder

Total surface area (T.S.A) $=616 \mathrm{~cm}^{2}$

$\Rightarrow \frac{\text { curved sur face area }}{\text { total sur face area }}=\frac{1}{2}$

⟹ CSA = 1/2 * TSA

⟹ CSA = 1/2 * 616

$\Rightarrow \mathrm{CSA}=308 \mathrm{~cm}^{2}$

Now,

TSA $=2 \pi r h+2 \pi r^{2}$

$\Rightarrow 616=\operatorname{CSA}+2 \pi r^{2}$

$\Rightarrow 616=308+2 \pi r^{2}$

$\Rightarrow 2 \pi r^{2}=616-308$

$\Rightarrow 2 \pi r^{2}=616-308$

$\Rightarrow 2 \pi r^{2}=308$

$\Rightarrow \pi r^{2}=308 / 2$

$\Rightarrow r^{2}=308 / 2 \pi$

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

⟹ r = 7 cm

Since, CSA $=308 \mathrm{~cm}^{2}$

$\Rightarrow 2 \pi \mathrm{rh}=308$

⟹ 2 * 22/7 * 7 * h = 308

⟹ h = 7cm

Volume of cylinder $=\pi r^{2} * h$

= 22/7 * 7 * 7 * 7

$=22 * 49=1078 \mathrm{~cm}^{2}$