Reading Activity

Circle Sector and Segment

circle sector segment

There are two main "slices" of a circle;:

The "pizza" slice is called a Sector..
And the Segment, which is cut from the circle by a "chord" (a line between two points on the circle).

Sector	Segment

The Quadrant and Semicircle are two special types of Sector:

Half a circle is
a Semicircle.

Quarter of a circle is
a Quadrant.

You can work out the Area of a Sector by comparing its angle to the angle of a full circle.

Note: We are using radians for the angles.

circular sector area

This is the reasoning:

A circle has an angle of 2π and an Area of:πr²

A Sector has an angle of θ instead of 2π so its Area is : θ2π × πr²

Which can be simplified to:θ2 × r²

Area of Sector = θ 2 × r² (when θ is in radians)

Area of Sector = θ × π 360 × r² (when θ is in degrees)

circular segment area

The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here).

There is a lengthy reason, but the result is a slight modification of the Sector formula:

Area of Segment = θ − sin(θ) 2 × r² (when θ is in radians)

Area of Segment = ( θ × π 360 − sin(θ)2 ) × r² (when θ is in degrees)

circular sector arc length

The arc length (of a Sector or Segment) is:

L = θ × r (when θ is in radians)

L = θ × π180 × r (when θ is in degrees)

A garden is in the shape of a semicircle with a diameter of 40m. What is the area of the garden?

Use 3.14 as an approximation for π