What is the surface area of a cylinder?
A cylinder is a solid figure with two circular, similar and parallel bases. The bottom of a cylinder is obtained through the top, by making a transfer in space. The circular bases are of equal size. The distance between the two bases is called the “height”.
The surface area of a cylinder is the area occupied by its surface in a three-dimensional space, in simpler terms, it’s what it would take to cover its surface. It is important to remember though that, if length is evaluated in meters and volume in cubic meters, the surface is represented in square units. The cylinder’s surface area is the sum of the area of both of its circular bases and its curved surface.
How do you find the surface area of a cylinder?
To understand how to find the surface area of a cylinder, think of it as a soda can. It has three surfaces; the top, the bottom and the piece that forms the sides of the can (which you can unroll and it will give you a rectangle). Now let’s understand the basics.
First of all, before calculating anything, you have to make sure that all of the measurements you have are in the same unit. As we have mentioned before, a cylinder has two types of surfaces, one is the curved surface and the other are the circular bases. So to find the total surface area, you must add up these two.
To find the surface area of a cylinder, calculate the surface area of each base, knowing that they are circles, the surface area of each circle is π x r², where r is the radius of the base of the circle. And as there are two circular bases, their combined surface area is 2 x π x r². Next, calculate the surface area of the curved side, which can be calculated by multiplying the circumference by the height or 2 x π x r x h , where r is the radius and h is the height of the cylinder.
Surface area of cylinder formula
Combining these two parts mentioned in the paragraph above will give us the formula of the surface area of a cylinder:
A = 2 x π x r² + 2 x π x r x h
A = 2 π r² + 2 π r h
Where:
π is pi = 3.142
r is the radius of the cylinder
h is the height of the cylinder
While calculating the surface area of a cylinder, remember that the radius and height must be in the same units, if they are not, convert them before you start your calculation.
Example 1 :
Let’s suppose we have a cylinder with a height of 9 cm and a circle radius of 3 cm. To find the surface area of this cylinder, we must find the area of its bases first, which in this example is:
A1 = 2 x π x r²
A1= 2 x 3.14 x 3²
A1 = 56.52 cm²
And now, let’s calculate the surface area of its side:
A2 = 2 x π x r x h
A2 = 2 x 3.14 x 3 x 9
A2 = 169.56 cm²
The surface area of this cylinder is the sum of A1 + A2 (add the areas) which is :
A = A1 +A2
A = 56.52 + 169.56
Therefore the surface area of this cylinder is :
A = 226.08 cm²
Example 2 :
In this example, the cylinder has a height of 7 cm and a circle radius of 5 cm.
To find the surface area of this cylinder, we must find the area of its base ends first:
A1 = 2 x π x r²
A1 = 2 x 3.14 x 5²
A1 = 157 cm²
Up next, let’s calculate the surface area of the curved side of the cylinder:
A2 = 2 x π x r x h
A2 = 2 x 3.14 x 7 x 5
A2 = 219.8 cm²
The surface area of this cylinder is found by adding A1 and A2 which gives us :
A = A1 +A2
A= 157 + 219.8
So, the volume of this cylinder is :
A = 376.8 cm