Question

If the sheet of dimension $10cm\times 2cm$ is rolled along the length to form a right circuar cylinder, then the volume of the cylinder in $c{m}^3$ is

• A. $\frac{20}{\pi }$
• B. $\frac{50}{\pi }$
• C. $\frac{25}{\pi }$
• D. $40\pi$

Answer 1

Answer: (B)

$\frac{50}{\pi }$

Given, Circumference of top of cylinder $=10$ $cm$
$\therefore 2\times \pi \times r=10$

$\therefore r=\frac{5}{\pi }$ $cm$

Height of cylinder $=2$ $cm$
So, Volume of cylinder $=\pi r^{2}h$
$=\pi \times {\left(\frac{5}{\pi }\right)}^2\times 2$

$=\pi \times \frac{25}{{\pi }^2}\times 2$

$=\frac{50}{\pi }c{m}^3$