Question

A rectangular piece of paper of dimensions $22cm$ by $12cm$ is rolled along its length to form a cylinder. The volume of the cylinder so formed is _____.

• A. $442c{m}^3$
• B. $402c{m}^3$
• C. $462c{m}^3$
• D. $460c{m}^3$

Answer 1

Answer: (C)

$\left(462c{m}^3\right)$

If a paper is rolled along its length to form a cylinder then,
height of the cylinder $\left(h\right)=$ breadth of paper $=12cm$

Circumference of the base of the cylinder $=$ length of paper
$\Rightarrow 2\pi r=22cm$, where $r$ is the radius of the cylinder.
$\Rightarrow r=\frac{22}{2\times \pi }$
$\Rightarrow r=\frac{22}{2\times \frac{22}{7}}$
$\Rightarrow r=\frac{7}{2}cm$

Volume of the cylinder $=\pi r^{2}h$
$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 12c{m}^3$
$=22\times 7\times 3$
$=462c{m}^3$