# The total surface area of a cylinder is 462 cm2.

Question:

The total surface area of a cylinder is 462 cm2. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder.

Solution:

Total surface area = 462 cm2

Given: Curved surface area $=\frac{1}{3} \times$ total surface area $=\frac{1}{3} \times 462=154 \mathrm{~cm}^{2}$

Now, total surface area - curved surface area $=2 \pi \mathrm{rh}+2 \pi \mathrm{r}^{2}-2 \pi \mathrm{rh}$

$\Rightarrow \Rightarrow 462-154=2 \pi r^{2}$

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

$\Rightarrow r^{2}=\frac{308 \times 7}{44}=49$

$\Rightarrow r=7 \mathrm{~cm}$

Now, curved surface area = 154 cm2

$\Rightarrow 2 \pi r h=154$

$\Rightarrow 2 \times \frac{22}{7} \times 7 \times h=154$

$\Rightarrow h=\frac{154}{44}=3.5 \mathrm{~cm}$

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

$=\frac{22}{7} \times 7^{2} \times 3.5$

$=539 \mathrm{~cm}^{3}$