Finding the area of a circle is an important thing for a Math student to know.
There can be a few different ways to approach finding the area.
How to Find the Area of a Circle
Working out the area of a circle isn’t overly difficult provided one remembers the correct formula, which is as follows.If you have a circle with radius r, then the area A is given by the the following formula.
Area of Circle = π × r2
Examples
(1.1)
Find the area of the following circle
Solution
Area = π × r2 => π × 62 = 113.1
The circle area is 113.1cm2.
(1.2)
Find the area for the following circles.
a) Circle with radius 2.8cm.
b) Circle with diameter 24m.
Solution
a) Area = π × 2.82 = 24.63cm2
b) As a circle diameter is double the radius, we have to divide 24m by 2 first, then use the formula.
24 ÷ 2 = 12, Area = π × 122 = 452.39cm2
Area of a Half Circle, Quarter Circle
Sometimes we want to establish the area of just part of a full circle.
However the complete circle area still generally needs to be established initially. Thus we still need to know how to obtain the area of a full circle.
Examples
(2.1)
The gap under a bridge creates in the following half circle, what is the area of this gap?
Solution
As the diameter is 14m, the radius is 7m.
The first step is to work out what the area of the full circle would be.
Area = π × 72 = 153.94m2
Now we only need to divide the full circle area by 2, in order to get the area of the gap below the bridge.
153.94m2 ÷ 2 = 76.97m2
(2.2)
For a the area of a quarter circle the overall approach is the same, but the total circle area will this time be divided by 4 rather than 2.
Area of the complete circle would be: π × 82 = 201.06m2
So the area of the quarter circle is as follows. 201.06 ÷ 4 = 50.27m2
Area of Circle using Circumference
Example
(3.1)
What is the area of a circle with a circumference of size 48cm ?
Solution
Here we first need to know the formula for obtaining the circumference of a circle, as this will assist us here in finding the size of the radius.
CIRCUMFERENCE = π × DIAMETER => 48 = π × DIAMETER
( divide both sides by π ) => \frac{\bf{48}}{\pi} = DIAMETER
DIAMETER = 15.28cm
RADIUS = 15.28cm ÷ 2 = 7.64cm
Now, AREA = π × ( 7.64 )2 = 183.37
The whole area of a circle with a circumference of 48cm is 183.37cm2.