Question

Which formula is used to calculate the curved surface area of a cylinder?
a.$\pi {r^2}$
b.$2\pi rh$
c.$2\pi {r^2}$
d.$2\pi r$

Answer 1

Hint: A cylinder is a $3$-D solid, in which the circular base and top are made parallel to each other.
The area of a cylinder is nothing but the space occupied by the cylinder. This area is of two types which are as follows.
Curved Surface Area- When we find the area for the curved surfaces leaving the circular base and top, it is said to be the curved surface area. It can be called the lateral surface area.
Total Surface Area-When we find the area of the curved surfaces as well as the bases, it is said to be the total surface area.
Here, our question is to find the formula for calculating the curved surface area.

Complete step by step answer:
 Now, we shall take a rectangular sheet of length l and breadth is same as the height $h$ of the cylinder. Then, we are going to cover the cylinder using the sheet. Now, we can note that the length of the sheet is the same as the circumference of the base of the cylinder $2\pi r$.

 So, the area of the sheet provides the curved surface area of the cylinder.
The curved surface area of the cylinder=Area of the rectangular sheet
\[ = length \times breadth\]
$ = circumference{\text{ }}of{\text{ }}the{\text{ }}base \times height$
$ = 2\pi rh$
Hence, the curved surface area of the cylinder $ = 2\pi rhsq.units$

Therefore, option b) is correct.

Note:
The area of a cylinder is nothing but the space occupied by the cylinder. Here, the area of the sheet provides the curved surface area of the cylinder. That is, Curved surface area of the cylinder=Area of the rectangular sheet
Hence, the curved surface area of the cylinder $ = 2\pi rhsq.units$