Question

How to derive the formula from the net of cyclinder to find its surface area?

Answer 1

The surface area of a cylinder can be found by breaking it down into three parts:

The two circles that make up the ends of the cylinder.

The side of the cylinder, which when "unrolled" is a rectangle

You can see that the cylinder is made up of two circular disks and a rectangle that is like the label unrolled off a soup can.

The area of each end disk can be found from theradius r of the circle. 
The area of a circle is πr2, so the combined area of the two disks is twice that, or2πr2. 
(See Area of a circle).

The area of the rectangle is the width times height. 
The width is the height h of the cylinder, and the length is the distance around the end circles. This is the circumference of the circle and is 2πr. Thus the rectangle's area is 2πr × h.

Combining these parts we get the final formula:

area

=

2

π

r

2

+

2

π

r

h

where:
π  is Pi, approximately 3.142
r  is the radius of the cylinder
h  height of the cylinder


By factoring 2πr from each term we can simplify this to

area

=

2

π

r

(

r

+

h

)

However, the first is the one shown in most textbooks and more clearly shows how it is derived

Answer 2

Answer:

TSA of cylinder = 2πr(r+h)

CSA of cylinder = 2πrh

Volume of cylinder =

${\pi \: r}^{2} h$

Step-by-step explanation:

Hope this helps mate