Areas of Circles
The formula for the area of a circle
To find the area of a circle, we need to square the radius and then multiply the result by pi (π).
π is an irrational number that is approximately equal to 3.14 or 22/7, if you prefer to work with fractions.
Let’s do a question:
What is the area of a circle if its radius is 15 cm?
A = πr2
A = π(15)2A = 225π
A = 706.5
The area of the circle is 706.5 cm2.
If you have the diameter and not the radius, you can divide the diameter by 2 to get the radius:
Find the radius by dividing the diameter by 2.
Let’s do a question:
What is the area of a circle if its diameter is 8 cm?
Since the circle’s diameter is 8 cm, its radius is 8 cm/2 = 4 cm.
A = πr2
A = π(4)2A = 16π
A = 50.24
The area of the circle is 50.24 cm2.
If we do not want to find the radius, we can calculate the area of the circle by multiplying the diameter by itself and then multiplying that result by 0.785. This is because, since r = d/2:
r2 = (d/2)2 = d2/4
Plugging this in for r2 in the formula for the area of a circle gives us (πd2)/4 = 0.785d2.Let’s make sure that this formula would give us the same area for the circle with a diameter of 8 cm:
A = 0.785d2
A = (0.785)(82)A = (0.785)(64)
A = 50.24
The area of the circle is 50.24 cm2. Yes, the area of the circle is the exact same as when it was found by dividing the diameter by 2 to get the radius and then using the formula A = πr2.
Since the radius or the diameter would be in cm, m, in., ft, km, etc., and the radius or the diameter is squared in the equation, the area of the circle will be in square units.
cm2, m2, in.2, ft2, km2, etc.
If you want to convert the units, you either need to convert them before you calculate the area, or you need to square the conversion factor (since the area’s units are square).
If you have a cylinder (like a pipe), you can multiply the area of the circle by the height of the cylinder to get the volume of the cylinder, which would be in cubic units.
When is the area of a circle used by water systems operators?
In calculations for water velocity in pipes.
In calculations of surface loading on clarifiers.
We need to know how to find the area of a circle to be able to find the volume of a cylinder, and calculating the volume of a cylinder is used to find the capacity of tanks and to determine the length of contact time that is provided by a cylindrical reservoir.
To find the capacity of a section of pipe.
Did you know that the only numbers that are irrational are non-repeating, non-terminating decimals?
Did you know that 100 trillion digits of pi have been found?
Here is a webpage that will calculate the area of a circle for you: https://www.omnicalculator.com/math/area-of-a-circle
Watch a video that explains the reason for the formula for the area of a circle.
Some good videos that explain how to calculate the area of a circle: