Question

A rectangular sheet of paper is $44$ cm long and $20$ cm wide. It is rolled along its length so that the breadth is in contact with each other. Find the volume of the cylinder so formed.

Answer 1

Let $r$ be the radius of the cross-section of cylinder and $h$ be the height of the cylinder.

According to question the rectangular sheet is rolled along its length

$\therefore$Circumference of crossection of cylinder $=$ Length of rectangular sheet

$\Rightarrow 2\pi r=44cm\Rightarrow r=\frac{44cm}{2\pi }$

$\Rightarrow r=\frac{44cm\times 7}{2\times 22}$

$\Rightarrow r=7cm$

Also, Height of cylinder $=$ breadth of rectangular sheet $=$ 20cm

Thus,

Volume of cylinder $=\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 20$

$=22\times 7\times 20$

Volume of cylinder $=3080c{m}^3$