Question

The total surface area of a solid cylinder is $462{cm}^2$. Its curved surface area is one third of total surface area. Find the volume of the cylinder.

• A. $229c{m}^3$
• B. $509c{m}^3$
• C. $439c{m}^3$
• D. $539c{m}^3$

Answer 1

The correct option is D $539c{m}^3$

Given:

$TSA=462c{m}^2=2\pi r(r+h)$

$CSA=2\pi rh=\frac{1}{3}\left(TSA\right)=\frac{1}{3}\times 462=154c{m}^2$

$\therefore TSA-CSA=2\pi r^2$

$\Rightarrow 308=2\pi r^2$

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

$\Rightarrow r=7cm$

$CSA=154=2\pi rh$

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

$\therefore 3.5cm=h$

$\therefore$ volume = $\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 3.5c{m}^3$

$=539c{m}^3$