Question:
A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.
Solution:
The length $(l)$ and breadth $(b)$ of the rectangular sheet are $44 \mathrm{~cm}$ and $20 \mathrm{~cm}$
Now, the sheet is rolled along the length to form a cylinder.
Let the radius of the cylinder be $r \mathrm{~cm}$.
Height, $h=b=20 \mathrm{~cm}$
Circumference, $S=44 \mathrm{~cm}$
$2 \pi r=44 \mathrm{~cm}$
$2 \times \frac{22}{7} \times r=44 \mathrm{~cm}$
$r=7 \mathrm{~cm}$
Volume of the cylinder, $\mathrm{V}=\pi r^{2} h$
$=\frac{22}{7} \times 7^{2} \times 20 \mathrm{~cm}^{3}$
$=3080 \mathrm{~cm}^{3}$