1. Circumference of a Circle
The circumference is the total distance around the circle. It is given by the formula:
C=2πr
where:
- C = Circumference
- rrr = Radius of the circle
- π ≈ 3.14159
Alternatively, if you know the diameter ddd of the circle (which is twice the radius), the formula can be written as:
C=πd
where:
- ddd = Diameter of the circle
2. Area of a Circle
The area is the space enclosed by the circle. It is given by the formula:
A=πr2
where:
- A = Area
- r = Radius of the circle
4. Length of an Arc
The length of an arc is a portion of the circle’s circumference. The formula for the length of an arc is:
L=θ/360∘×2πrL
where:
- L = Length of the arc
- θ = Central angle (in degrees) subtended by the arc
- r = Radius of the circle
If θ is in radians, the formula is: L=θr
where θ is the angle in radians.
5. Area of a Sector
The area of a sector of a circle is the area of a “slice” of the circle, which is proportional to the central angle. The formula is:
Asector=θ/360∘×πr2
where:
- Asector = Area of the sector
- θ= Central angle (in degrees)
If θ\thetaθ is in radians, the formula becomes:Asector=12θr2A_{\text{sector}} = \frac{1}{2} \theta r^2Asector=21θr2
where θ\thetaθ is in radians.