Question

A solid cylinder has a total surface area of $462$ $c{m}^3$ Its curved surface area is one-third of its total surface area . The volume of the cylinder is :$(\pi =\frac{22}{7})$

• A. $792$ $c{m}^3$
• B. $539$ $c{m}^3$
• C. $495$ $c{m}^3$
• D. $676$ $c{m}^3$

Answer 1

Answer: (B)

$539$ $c{m}^3$

TSA$=462c{m}^2$, CSA$=\frac{1}{3}\times 462=154c{m}^2$

$\therefore$Area of each circle$=\frac{1}{2}(TSA-CSA)$

$\Rightarrow \pi r^2=\frac{1}{2}(462-154)$

$\Rightarrow \pi r^2=154$

$\Rightarrow r^2=\frac{154\times 7}{22}=49$

$\Rightarrow r=\sqrt{49}=7cm$

$\therefore 2\pi rh=154\Rightarrow h=\frac{154\times 7}{2\times 22\times 7}=3.5cm$

$\therefore$Volume $=\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 3.5=539c{m}^3$