Sector of a Circle: Definition & Formula

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  • 0:00 Radii & Sectors
  • 0:50 Common Sectors
  • 1:11 Major & Minor Sectors
  • 1:34 Area of a Sector
  • 2:26 Examples
  • 3:54 Lesson Summary
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Lesson Transcript
Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will discuss sectors of a circle and how to find the area of a sector. You will learn the different parts that make up a sector and test your skills with practice problems.

Radii & Sectors

We've all had a slice of pie or a piece of pizza. Both are real life examples of a sector of a circle. A sector is a wedge of a circle made from two radii. Radii, the plural of radius, are line segments that start on the outside and end at the center of the circle. Think of radii as cuts from the crust of the pizza to the middle.

Image 1: Sector of a circle made from two radii

Image 1 shows an example of a sector in red. This is a sector because the line segments extending from point A to point O and from point B to point O are radii. Radii must touch the outside and the center of a circle. Image 2 shows a non-example of a sector because it is not made of two radii. The line segment goes right across the circle and never meets the center. Pizzas slices are typically not cut like this.

Image 2: Non-example of a sector of a circle

Commonly Sectors

When you open a pizza box, you typically find that your pizza is cut into six or eight pieces. Similarly, circles are often cut into halves and quarters, and special names are given to these types of sectors. When a circle is cut in half, those sectors are called semicircles. When a circle is cut into fourths, those sectors are called quarter circles or quadrants.

Major & Minor Sectors

When two radii meet at the center of a circle to form a sector, they actually form two sectors. One of the sectors is larger than the other, unless they are both semicircles in which case they are the same size. The larger sector is called the major sector and the smaller sector is called the minor sector. In Image 1, you can see the minor sector is in red and the major sector is in white.

Area of a Sector

Imagine that you're really hungry and want a slice of pizza that is larger than your friend's slice. You may be able to figure out which is bigger just by looking at them, but there is also a mathematical way to figure out size. The formula for area of a sector is based on the formula for the area of a circle, except that you're calculating the are for a part of a circle instead of the whole.

Image 4: Formula for the area of a sector

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