Introduction
The very common measurements, of a circle, are circumference of circle, area of circle, area of sector, length
of arc and area of segment.
So, let’s discuss them and see how to calculate them.
Circumference of circle
Circumference is distance around the circle. Its units are the 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 = 2πr
where, π is a constant value and r is radius of circle
The constant value of π =
or 3.14
Calculate circumference of circle whose radius is 5cm.
Here, radius of circle = 5cm
As we know, Circumference of circle = 2πr
∴ Circumference of circle = 2π × 5
= 2 × 3.14 × 5
= 31.4 cm
What is π?
π 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 the circle to the diameter of the circle.
It is a ratio of circumference and diameter of a circle.
This constant value is denoted by π and read as pi.
π =
Area of circle
Area of circle is a space occupied by a circle. Its units are i.e meter2, centimeter2, millimeter2 etc.
Area of circle = πr2
where, π is a constant value and r is radius of circle
Again, the constant value of π =
or 3.14
Calculate area of circle whose radius is 10cm.
Here, radius of circle = 10cm
As we know, Area of circle = π2
∴ Area of circle = π × 102
= 3.14 × 100
= 314 cm2
For the following below measurements, please refer to this figure.
Area of sector
Area of sector of angle θ = × π r2
Area of major sector
Area of major sector OADB = πr2 – Area of minor sector OACB
Length of arc
Length of arc of sector of angle θ = × 2 π r
Area of segment
Area of segment ACB = π r2 – Area of triangle
Area of major segment
Area of major segment ADB = π r2 – Area of minor segment ACB