Area Of A Circle Sector Guide
Hi there. In this math guide, I cover the area of a circle sector. For the screenshots I use the Math Is Fun online whiteboard and witeboard.com.
Topics
- Review Of Area Of Circle
- Sector of Circle
- Area Of Circle Sector With Examples
Review Of Area Of Circle
Before getting into the area of a circle sector it is good to review the area of a circle. Given the radius of the circle r
, the area of the circle is given by Area = πr²
.
If you are given the diameter of the circle, talk half the length of the diameter (d)
to obtain the circle's radius.
Sector of Circle
The sector of a circle refers to the part of the circle given an angle from 0 degrees to 360 degrees. In radians, the angle is from 0 to 2π
. (π is pi) Picture taken from https://byjus.com/maths/area-of-sector/.
Area Of Circle Sector With Examples
For the area of the circle, the formula is given by the area of the circle multiplied by the fraction of the angle divided by a full rotation of 360 degrees (or 2π). The symbol θ (theta) is used to represent the angle for the sector of a circle.
Note that Pi (π) radians is equal to 180 in degrees.
Example One
Given an angle of 30 degrees in a circle and a radius of 8 centimetres, what is the area of the orange sector of the circle?
Example Two
A circle has a radius of 10 metres and an angle of π/4
radians, what is the area of the sector of the circle?
Example Three
The area of the sector of the circle is 3π/2
square units. This circle has a radius of 3 units. What is the angle of the circle sector?
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