Knowing how to find the area of a circle is an important skill for a Math student to have.
Here at mathzenith, we show you how.
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 × 42 = 50.27
The circle area is 50.27cm2.
1.2
Find the area for the following circles.
a) Circle with radius 6cm.
b) Circle with radius 2.4cm.
c) Circle with diameter 30m.
Solution
a) Area = π × 62 = 113.1cm2
b) Area = π × 2.42 = 18.1cm2
c) As the diameter is double the radius, we just have to divide 30m by 2 first, then apply the formula.
30 ÷ 2 = 15, Area = π × 152 = 706.86cm2
How to Find Area of a Half Circle, Quarter Circle
Sometimes the requirement is to establish the area of only part of a full circle.
However the whole circle area still usually needs to be established initially. So we still need to know how to find the area of a circle.
Examples
2.1
The opening under a large bridge results in the following half circle, what is the area of this opening?
Solution
As the diameter is 10m, the radius is 5m.
The first step is to establish what the area of the full circle would be.
Area = π × 52 = 78.54m2
Now we just need to divide the full circle area by 2 to get the area of the opening under the bridge.
78.54m2 ÷ 2 = 39.27m2
2.2
For a quarter circle the overall approach is the same, but the whole circle area will this time be divided by 4 instead of 2.
Area of the full circle whole would be: π × 92 = 254.47m2
Thus the area of the quarter circle is as follows. 254.47 ÷ 4 = 38.49m2
Area of a Circle, Further
Examples
3.1
A tarmac cycling race track is 8 metres wide, and has a diameter of 40 metres.
What is the area of the cycling race track tarmac part?
Solution
The area of the tarmac cycling track will be. ( Area of Outer Circle ) − ( Area of Inner Circle )
From the details in the diagram, it can be understood that the outer circle has a radius of 20 metres.
While the radius of the inner circle is. ( 40m − 8m − 8m ) ÷ 2 = 24m ÷ 2 = 12m
Area of outer circle = π × 202 = 1256.64m2
Area of inner circle = π × 122 = 452.39m2
Total area of tarmac cycling track = 1256.64m2 − 452.39m2 = 804.25m2
3.2
What is the area of a circle that has a circumference of 60cm ?
Solution
Here we initially need to know the formula for the circumference of a circle, as this will help us find the size of the radius.
CIRCUMFERENCE = π × DIAMETER => 60 = π × DIAMETER
( divide both sides by π ) => \frac{\bf{60}}{\pi} = DIAMETER
DIAMETER = 19.10cm
RADIUS = 19.10cm ÷ 2 = 9.55cm
Now, AREA = π × ( 8.05 )2 = 288.58
The total area of a circle with circumference 60cm is 208.58cm2.