Question

The curved surface area of a cylinder is $176c{m}^2$ and its base area is $38.5c{m}^2$. Find the volume of the cylinder and justify your answer.
[Use $\pi =\frac{22}{7}$]

Answer 1

Let the base radius be $r$ and the height of the cylinder be $h$.

Given, Base area of the cylinder$=38.5c{m}^2$
$\Rightarrow \pi \times r^2=38.5$
$\Rightarrow \frac{22}{7}\times r^2=38.5$
$\Rightarrow r^2=38.5\times \frac{7}{22}$
$\Rightarrow r=\sqrt{12.25}$
$\therefore r=3.5cm$
Curved surface area of a cylinder $=176c{m}^2$
$\Rightarrow 2\pi rh=176$
$\Rightarrow 2\times \frac{22}{7}\times 3.5\times h=176$
$\Rightarrow h=\frac{176\times 7}{2\times 22\times 3.5}$
$\therefore h=8cm$

So, the volume of the cylinder is $=\pi r^{2}h$
$=\frac{22}{7}\times (3.5{)}^2\times 8$
$=308c{m}^3$.