Question

The volume of a cylinder is $308c{m}^3$. Its height is $8cm$. Find its lateral surface area and total surface area.

Answer 1

Let $r$ be the radius of cylinder.

Volume of cylinder $=308{cm}^3=\pi r^{2}h$

$\Rightarrow \frac{22}{7}\times r^2\times 8=308$

$\Rightarrow r^2=\frac{308\times 7}{22\times 8}$

$\Rightarrow r=\sqrt{\frac{49}{4}}=\frac{7}{2}cm$

Therefore,

Lateral surface area of cylinder $=2\pi rh=2\times \frac{22}{7}\times \frac{7}{2}\times 8=176{cm}^2$

Also,

Total surface area of cylinder $=2\pi r(h+r)=2\times \frac{22}{7}\times \frac{7}{2}\times (8+\frac{7}{2})=22\times \frac{23}{2}=253{cm}^2$