Question

A rectangular piece of paper is $22$ cm long and $10$ cm wide A cylinder is formed by rolling the paper along its length Find the volume of the cylinder

• A. $175$ $c{m}^3$
• B. $75$ $c{m}^3$
• C. $125$ $c{m}^3$
• D. $275$ $c{m}^3$

Answer 1

Answer: (A)

Length of the rectangular paper will be height of the cylinder and width of the rectangular paper is circumference of the cylinder
$\Rightarrow 2\pi r=10cm$

$\Rightarrow r=\frac{10}{2\pi }cm$ and $h=22cm$

Now,

Volume of the cylinder $=\pi r^{2}h$
$=\pi \times \frac{10}{2\pi }\times \frac{10}{2\pi }\times 22c{m}^3$

$=5\times \frac{5}{\frac{22}{7}}\times 22c{m}^3$

$=25\times \frac{7}{22}\times 22c{m}^3$

$=25\times 7c{m}^3$

$=175c{m}^3$

Hence, Option A is correct.