# Arc Length and Area of Sectors

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In this lesson we look at the fractions of circles which are called “Sectors”.

We cover how to find the “Arc Length” and the “Area” of these sectors.

This lesson assumes that people already know how to calculate the “Circumference” and the “Area” of a Circle.

If you need to revise Circumference and Area, then take a look at our previous lessons at the following links:

http://passyworldofmathematics.com/circumference/

http://passyworldofmathematics.com/area-of-a-circle/

Definition of a Sector

A sector is a piece of a circle that is cut out along two radiuses (radii).

If it is shaped like a single slice of pizza, it is a “Minor” sector.

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If the Sector is shaped like a yellow Pacman, then it is a “Major” Sector.

Eg. The large remaining section of Pizza in the above picture is a MAJOR sector, because it is between one half circle and a full circle in size.

Quarter Circles and Half Circles are also “Sectors”.

Sectors should be familiar to anyone who has ever drawn a Pie Chart.

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It is important not to confuse “Sectors” with “Segments”, which are a different type of fraction of a full circle.

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Sectors in the Real World

Sectors are important for designing and building Freeway exits, when they use a “Clover Leaf” style Interchanges.

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Sectors are also found on hard drives in computers. However these “sectors” are slightly different to the ones we do in Mathematics, as they are actually not a full sector, but part of a math sector that is between two circular “tracks”.

Arc Length for a Sector

For a sector, we can find how long it’s curved part is, by working out the fraction of a full circle we are dealing with.

The following video explains what a sector is, and how to calculate its Arc Length.

This next video shows three Arc Length examples

Sector Arc Length Example 1

The following example shows how to find the Arc Length of a “Minor” sector.

A Minor Sector is basically a small part of a circle, such as a single piece of Pizza.

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Sector Arc Length Example 2

This example shows how to calculate the Arc Length for a “Major” sector.

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Area of a Sector

The following video shows how to calculate the Area of a Sector.

The next video also shows how to calculate the Areas of Sectors.

Sector AREA – Example 1

The following example shows how to calculate the AREA contained inside a “Minor” sector.

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Sector AREA – Example 2

This example shows how to calculate the AREA for a “Major” sector.

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Video on Arc Length and Areas of Circles

The following video provides examples of both Arc Length and Sector Area calculations.

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