Area of a Sector of a Circle
(KS3, Year 7)
In this formula, θ is the angle (in degrees) of the sector and r is the radius of the circle. The image below shows what we mean by the area of a sector:
How to Find the Area of a Sector of a Circle
Finding the area of a sector of a circle is easy.Question
What is the area of the sector with an angle of 72° and a radius of 5 cm, as shown below?
Step-by-Step:
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Substitute the angle and the radius into the formula. In our example, θ = 72° and r = 5.
Area of sector = 72°⁄360° × π × 5 × 5
Area of sector = (72° ÷ 360°) × 25 × π
Area of sector = 15.7 cm2
Answer:
The area of a sector of a circle with a radius of 5 cm, with an angle of 72°, is 15.7 cm2.What Is a Sector?
A sector is a region of a circle bounded by two radii and the arc lying between the radii.
Why Does the Formula Work?
The area of a sector is just a fraction of the area of the circle of the same radius. The area is given by πr2, where r is the radius. For example, a sector that is half of a circle is half of the area of a circle.
A sector that is quarter of a circle has a quarter of the area of a circle.
In each case, the fraction is the angle of the sector divided by the full angle of the circle.
When measured in degrees, the full angle is 360°.
Hence for a general angle θ, the formula is the fraction of the angle θ over the full angle 360° multiplied by the area of the circle:
Area of sector = θ⁄360° × πr2
Beware
Is the Angle Given in Degrees or Radians
The formula to find the length of a sector of a circle depends on whether the angle at the center of the sector is given in degrees or radians. Make sure you check what units the angle is given in.
This page was written by Stephen Clarke.
Worksheet
This test is printable and sendable
