Area Of A Circle Sector Guide

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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 . (π is pi) Picture taken from https://byjus.com/maths/area-of-sector/.

Sector-Of-A-Circle-2-1.png

 

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.

formula_sectorAreaCircle.PNG

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_one.PNG


example_one_calculations.PNG

 

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_two.PNG


example_two_calculations.PNG

 

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?


example_three_calculations.PNG

 

Thank you for reading.

Posted with STEMGeeks



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