**Curved surface area of Cylinder**

Cylinder is the three-dimensional geometrical object which is having two circular bases with fixed radius which are joined by a curved surface as shown in figure.

The line joining the centers of two circular bases is called as the axis of cylinder.

And the perpendicular distance between these two centers of circular bases of cylinder is the height of the cylinder as shown in figure.

And the area of curved surface joining the two circular bases of cylinder is called as the curved surface area.

**Derivation for Curved Surface area of Cylinder:**

- Let us consider the cylinder with two circular bases having radius r and height h.
- To find the curved surface area of a cylinder, we take a rectangular paper if we roll it then it will form the cylinder.
- If l is the length and b is the breadth of the rectangular plane then after forming cylinder the breadth b becomes the height of the cylinder now.
- And the length of the rectangular plane forms the circumference of circle forming the cylinder.

Hence, the curved surface area of cylinder = surface area of rectangular plane

= length*breadth

= l*b

But, here after forming the cylinder from rectangular paper,

Breadth = height of cylinder = h and

Length = circumference of circle = 2*π*r

Thus, the curved surface area of cylinder of height h, and circular bases having radius r is given by,

Curved surface area of cylinder = l*b

= 2πrh

Curved surface area of cylinder = 2*π*r*h

Hence proved.