There are separate formulae for the area and perimeter of a circle. These formulae can also be applied to find the length of arcs and area of sectors.
Area and circumference of a circle
The circumference is the name given to the perimeter of the circle.
The area and circumference of a circle are given by the formulae:
Area=πr2
Circumference=2πr=πd
Where r is the radius of the circle, and d is the diameter.
Example 1
What is the area and perimeter of a circle that has a diameter of 10m?
Substitute d=10 into the formula for the circumference:
C=πd=10π
Circumference=(10π)m
For the area, first find the radius by halving the diameter:
r=d÷2=10÷2=5
Substitute r=5 into the formula for the area:
A=π×r2=π×52=25π
Area=(25π)m2
Labelling parts of a circle
These are the main parts of a circle you need to know:
name
description
illustration
Arc
A curved line that is part of the circumference
Sector
A portion of the circle that is divided by two radii (plural of radius)
Chord
A line that joins two points on the circumference
Segment
A part of the circle that is enclosed by a chord and an arc
Area and perimeter of arcs and sectors
It's possible to apply the formula for the area and circumference of a circle to arcs and sectors.
Lengthofanarc=360θ×circumference=360θ×2πr
Areaofasector=360θ×areaofcircle=360θ×πr2
Example 2
In the diagram below, the angle between the two radii is 45∘. The radius of the circle is 4cm. What is the length of the arc and area of the shaded sector?
The sector of a circle is a portion of the circle that is bounded by two radii.
What is the formula for the area of a circle?
The formula for the area of a circle is πr^2, where r is the radius.
What is the circumference of a circle?
The circumference is the name given to the perimeter of the circle. The formula to calculate it is 2πr or πd, where r is the radius and d is the diameter.