Question

The lateral surface area of a cylinder is equal to:-
A. \[2\pi {{r}^{2}}\]
B. \[2\pi r{{h}^{2}}\]
C. \[2\pi rh\]
D. None

Answer 1

Hint: Lateral surface area is also known as curved surface area. It is generally asked to find out the curved surface area or the lateral surface area for a solid which has a curved surface such as cylinder, cone, sphere, hemisphere, etc.

Complete step-by-step answer:

As mentioned in the hint that lateral surface area is also known as curved surface area and we are asked in general, to find out the curved surface area or the lateral surface area for a solid which has a curved surface such as cylinder, cone, sphere, hemisphere, etc.
Now, we know that on rolling a rectangular sheet of paper we get a solid figure. This figure is nothing but a cylinder which is open from the top and bottom.
Now, as we are concerned just with the lateral or the curved surface of the solid so we can avoid the top and bottom surfaces for now.
Now, as we know that the open cylinder is formed from the rectangular sheet of paper, we also know that the height of the cylinder is equal to the breadth of the rectangular sheet and the circumference of the cross section of the cylinder is formed of the entire length of the same rectangle.
If we now see closely, we will notice that if we know the area of that rectangular sheet, then we also know the lateral surface area of the cylinder.
Let the breadth of the sheet be ‘h’ and the length of it be \[2\pi r\] .
Now, we know that area of a rectangle is
\[\begin{align}
  & length\times breadth \\
 & So,\ 2\pi r\times h \\
 & 2\pi rh \\
\end{align}\]

Hence, the lateral surface area of the cylinder is \[2\pi rh\] .

Note: - We could have done the question other way round as well by considering an open cylinder with radius ‘r’ and height ‘h’ and then cutting the cylinder open and then forming a rectangular sheet from it with the breadth of the sheet as ‘h’ and the length of it as \[2\pi r\].