Area and Perimeter of Circle
Introduction
The very common measurements that can we do for a circle are circumference of circle, area of circle, area of sector, length of arc and area of segment.
So, let’s discuss about them and see how to calculate them.
Circumference of circle
Circumference is distance around the circle. Its units are same as that of length i.e meter, centimeter, millimeter etc.
We can calculate the circumference of circle using the formula as below:
Circumference of circle = \(2 \pi r\)
where, \(\pi\) is a constant value and r is radius of circle
The constant value of \(\pi = \frac{22}{7}\) or \(3.14\)
Calculate circumference of circle whose radius is 5cm.
Here, radius of circle = 5cm
As we know, Circumference of circle = \(2 \pi r\)
\(\therefore\), Circumference of circle = \(2 \pi \times 5\)
\(= 2 \times 3.14 \times 5\)
\(= 31.4 \; cm\)
What is \(\pi\)?
\(\pi\) is a value that never changes. If calculated, it always remains constant i.e. \(3.14\).
How is it calculated?
It is calculated by dividing the circumference of circle to diameter of circle.
It is a ratio of circumference and diameter of circle.
This constant value is denoted by \(\pi\) and read as pi.
\(\pi = \frac{Circumference}{Diameter}\)
Area of circle
Area of circle is a space occupied by a circle. Its units are i.e \(meter^2\), \(centimeter^2\), \(millimeter^2\) etc.
Area of circle = \(\pi r^2\)
where, \(\pi\) is a constant value and r is radius of circle
Again, the constant value of \(\pi = \frac{22}{7}\) or \(3.14\)
Calculate area of circle whose radius is 10cm.
Here, radius of circle = 10cm
As we know, Area of circle = \(\pi r^2\)
\(\therefore\), Area of circle = \(\pi \times 10^2\)
\(= 3.14 \times 100\)
\(= 314 \; cm^2\)
For the following below measurements, please refer to this figure.
Area of sector
Area of sector of angle \(\theta\) = \(\frac{\theta}{360} \times \pi r^2\)
Area of major sector
Area of major sector OADB = \(\pi r^2\) – Area of minor sector OACB
Length of arc
Length of arc of sector of angle \(\theta\) = \(\frac{\theta}{360} \times 2 \pi r\)
Area of segment
Area of segment ACB = \(\pi r^2\) – Area of triangle
Area of major segment
Area of major segment ADB = \(\pi r^2\) – Area of minor segment ACB