Surface Area of a Cylinder

A cylinder is one of the most basic structures that one deals with while studying geometry, and it is necessary to know, how to find the surface area of a cylinder if, you wish to clear your mathematics exam. Many people argue that such formulae and equations have no practical use in life, but some people do find this useful at some time or the other. All you need to do is memorize the formula for surface area of a cylinder, and you are good to go.

If you are wondering about the formula for surface area of a cylinder then you probably, know what the cylindrical shape looks like. So, in order to calculate surface area of a cylinder you need to know the value of two measurements of the geometrical shape. The first amount you need to know is the radius of the circles on both ends of the cylinder. This value is known as 'r'. The next value that you must know, in order to find the volume and surface area of a cylinder is the distance between the centers of both the circles. This value is known as 'h'.

In order to know, how to find the surface area of a cylinder you simply have to take these amounts and apply them to a particular formula.

Formula for Surface Area of a Cylinder
In order to know, what is the surface area of a cylinder you have to calculate the area for both the circles, and the cylindrical part in between. The cylindrical part, in between, is simply a rectangle that has been rolled up.

The area of the two circles on either end is known as the lateral surface area of a cylinder. The formula for the area of a circle is Πr². The value Π, or pi, is a mathematical number calculated as 22/7, or 3.14. Therefore, after using the formula and getting a number as its result, to find the total lateral surface area of a cylinder we simply multiply this number by 2.

Hence, the formula for the lateral surface area of a cylinder is 2Πr².

Next, we need to find the area of the rolled up rectangular part of the cylinder. This is known as the curved surface area of a cylinder. To find this area, we have to multiply the length of this rectangle with the breadth of the rectangle. The length is the same as the height of the cylinder h that we measured earlier, and the breadth is 2Πr.

Hence, the formula for the curved surface area of a cylinder is 2Πrh.

Equation for Surface Area of a Cylinder
Now, in order to find the total surface area of a cylinder all we need to do is add up these two amounts, that is, the curved surface area and the lateral surface area.

Here's how to find the surface area of a right cylinder which as a cylinder whose base is perpendicular to its sides.

Total Surface Area = 2Πrh + 2Πr²
Total Surface Area = 2Πr(h + r)

Example
Assume that there is a cylinder with radius 5 cm and height 10 cm. Therefore, r = 5, and h = 10.

Now, lateral surface area = 2Πr² = 2 X 22/7 X 5 X 5 = 157.14

Curved surface area = 2Πrh = 2 X 22/7 X 5 X 10 = 314.28

Therefore, total surface area = 314.28 + 157.14 = 471.42 cm²

Alternately you can apply the formula for total surface area directly as well.

Total surface area = 2Πr(h + r) = 2 X 22/7 X 5 (10 + 5) = 2 X 22/7 X 5 X 15 = 471.42 cm²

This was the formula for calculating the total surface area of a cylinder, and this can come in handy many times.