Question

A solid cylinder has total surface area of $462c{m}^2$. Its curved surface area is one-third of its total surface are. Find the volume of the cylinder (Take $\pi =\frac{22}{7}$)

• A. $224$
• B. $845$
• C. $664$
• D. None of the above

Answer 1

The correct option is D None of the above

Given, total surface area of cylinder = 462 square cm.

Also, CSA of cylinder $=\frac{\text{TSA of cylinder}}{3}$

$\Rightarrow TSA=2\pi rh+2\pi r^2\Rightarrow TSA=CSA+2\pi r^2\Rightarrow TSA=\frac{TSA}{3}+2\pi r^2\Rightarrow \frac{2TSA}{3}=2\pi r^2\Rightarrow \frac{TSA}{3}=\pi r^2\Rightarrow \frac{462}{3}=\frac{22}{7}\times r^2\Rightarrow r=7cm$

Now, CSA of cylinder $=\frac{\text{TSA of cylinder}}{3}=\frac{462}{3}=154c{m}^2$

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

Therefore, volume of the cylinder $=\pi r^{2}h$

$=\frac{22}{7}\times 7^2\times \frac{7}{2}=539c{m}^3$

Hence, volume of the solid cylinder is $539c{m}^3$.