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Surface Area of a Cylinder

A cylinder has a curved surface and two end faces. An example of a cylinder would be a can of soup, or a can or Pepsi or Coke.

Imagine that you are unwrapping the paper label from a can of soup. You will get a rectangle when you open the label. The width of this rectangle is equal to the height of the can. And its length is equal to the perimeter of the curved surface of the can. In addition, you have the two bases which are circles.

This breakdown of a cylinder can be shown pictorially as follows:

parts of a cylinder

 

So the surface area of a cylinder – represented by S – is the sum of the area of the two bases and the area of the curved surface.

S  =  area of the base circle + area of the curved surface + area of the top circle

=  pi r^2~+~2pi rh~+~pi r^2

=  2pi r^2~+~2pi rh

=  2pi r(r~+~h)

 

Now let us look at a few examples to calculate the surface area of a cylinder.

1. Calculate the surface area of a cylinder with a radius of 7 cm and a height of 12 cm.

S  =  2pi r^2~+~2pi rhsurface area of a cylinder_1

=  (2~*~pi~*~7^2)~+~(2~*~pi~*~7~*~12)

=  (2~*~22/7~*~7^2)~+~(2~*~22/7~*~7~*~12)

=  (2~*~22~*~7)~+~(2~*~22~*~12)

=  308 + 528

=  836 cm2

 

2. Calculate the surface area of a cylinder with a diameter of 10 cm and a height of 14 cm (correct to 1 decimal place).

S  =  2pi r^2~+~2pi rh

=  (2~*~3.14~*~5^2)~+~(2~*~3.14~*~5~*~14)  (since r = 5)

=  (2~*~3.14~*~25)~+~(2~*~3.14~*~70)

=  157 + 439.6

=  596.6 cm2