Question

A rectangular sheet of paper 44 cm $\times$ 20 cm is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.

Answer 1

Hint:Using the concept that the rectangular piece of paper is rolled along its length, the length of the piece of paper forms the circumference of the base of the cylinder and breadth of paper forms the height of the cylinder.Substituting these values in volume of cylinder formula we get required answer.

Complete step-by-step answer:
When the rectangular piece of paper is rolled along its length, the length of the piece of paper forms the circumference of the base of the cylinder and the breadth of paper forms the height of the cylinder.
Length of the rectangular piece of paper is 44 cm and width of the rectangular paper is 20 cm
Let us say that the circular discs are stacked up to the height. Now, the volume of the cylinder will be the product of the base area of the discs and the height.
The whole length of the circular base = circumference of the circular base = 44 cm.
The circumference of the circular base $=2\pi r$
$44=2\pi r$
Dividing both sides by 2, we get
$22=\pi r$
Put the value of the $\pi =\dfrac{22}{7}$ , we get
$22=\dfrac{22}{7}(r)$
Dividing both sides by 22, we get
$1=\dfrac{1}{7}(r)$
$7=r$
$r=7$
The area of the circular base $=\pi {{r}^{2}}$
The area of the circular base $=\dfrac{22}{7}\times {{\left( 7 \right)}^{2}}=22\times 7=154$
Height of the cylinder = width of the rectangular paper = 20 cm.
The volume of the cylinder = $154\times 20=3080$ .
Hence the volume of the cylinder is 3080 $c{{m}^{3}}$.

Note: Alternatively, you could substitute the radius and height of the cylinder directly into the formula for volume of the cylinder $\left( V=\pi {{r}^{2}}h \right)$ we get the same answer.