Question

The curved surface area of a cylinder is $176{cm}^2$ and its base area is $38.5{cm}^2$. Find the volume of the cylinder and justify your answer.

Answer 1

Base area of cylinder $=\pi r^2=38.5{cm}^2\left(\text{Given}\right)$

$\Rightarrow \pi r^2=38.5$

$\Rightarrow r^2=\frac{38.5\times 7}{22}$

$\Rightarrow r=\sqrt{12.25}=3.5cm$

CSA of cylinder $=2\pi rh=176{cm}^2\left(\text{Given}\right)$

$\therefore 2\pi rh=176$

$\Rightarrow h=\frac{176\times 7}{2\times 22\times 3.5}=8cm$

Therefore,

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

$=\frac{22}{7}\times {\left(3.5\right)}^2\times 8=308{cm}^3$