# Formula for Surface Area of cylinder – Derivation and Example

Here you will learn formula for surface area of cylinder (total surface area and curved surface area) with examples.

Let’s begin –

## Formula for Surface Area of cylinder

### (a) Total Surface Area

T.S.A = $$2\pi r(h + r)$$

### (b) Curved Surface Area

C.S.A = $$2\pi rh$$

#### Derivation :

Let take a rectangular sheet. The rectangular sheet when folded becomes a cylinder as shown in figure. The area of the rectangular sheet gives the curved surface area of the cylinder. Note that the length of the sheet is equal to the circumference of the circular base of cylinder which is equal to 2πr.

So, the curved surface area of the cylinder = area of the rectangular sheet = \length\times breadth\) = 2πr × h

Therefore,the Curved Surface Area of Cylinder = $$2\pi rh$$

In the case of a cylinder, unless stated otherwise, ‘radius of a cylinder’ means base radius of the cylinder.

If top and the bottom of the cylinder are also to be covered, then we need two circles to do that, each of radius r, and thus having an area of $$\pi r^2$$. giving us the total surface area of cylinder as $$2\pi rh$$ + $$2πr^2$$ = 2πr(r + h).

So, the Total Surface Area of Cylinder = 2πr(r + h).

where r  and h is the radius of the base of cylinder and height of cylinder respectively.

Example : Nandini had to make cylindrical object. She wanted to use cover curved surface of object with chart paper. What is the area of chart paper required, if she wanted to make object of height 15 cm with a 3.5 cm radius?

Solution : Radius of the base of the cylindrical object (r) = 3.5 cm.

Height of object (h) = 15 cm.

Area of the chart paper required = curved surface area of the object

= 2πrh = $$2\times {22\over 7}\times 3.5 \times 15$$

= 330 $$cm^2$$