Question

A solid cylinder has a total surface area of $231c{m}^2$. Its curved surface area is $\frac{2}{3}$ of the total surface area. Find the volume of the cylinder.

Answer 1

Given:
Total surface area of cylinder is $231c{m}^2$.
$\because$ curved surface area is $\frac{2}{3}$ of the total surface area.

$\therefore 2\pi rh=\frac{2}{3}\times 231c{m}^2=154c{m}^2\dots .\left(1\right)$

Also difference of T.S.A and C.S.A $=(231-154)c{m}^2$

$2\pi r(r+h)-2\pi rh=77$

$2\pi r^2=77$

$\therefore r=\sqrt{\frac{77\times 7}{44}}=\frac{7}{2}cm$

By substituting the value of $r$ in (1), we get

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

$\therefore h=\frac{154}{22}=7cm$

Volume of the cylinder $=\pi r^{2}h=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times 7=269.5$

Hence, the volume of the cylinder is $269.5c{m}^3$