How To Find The Central Angle Of A Sector

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 circumvolve by a "chord" (a line between two points on the circle).

The Quadrant and Semicircle are ii special types of Sector:

Half a circumvolve is
a Semicircle.

Quarter of a circle is
a Quadrant.

You lot 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 circumvolve has an bending of 2π and an Area of: πrⁱⁱ

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

Which tin can be simplified to: θ two × rⁱⁱ

Area of Sector = θ two × rⁱⁱ (when θ is in radians)

Area of Sector = θ × π 360 × r^two (when θ is in degrees)

circular segment area

The Expanse of a Segment is the expanse of a sector minus the triangular slice (shown in light blue here).

At that place is a lengthy reason, just the result is a slight modification of the Sector formula:

Surface area of Segment = θ − sin(θ) ii × r² (when θ is in radians)

Area of Segment = ( θ × π 360 − sin(θ) two ) × rⁱⁱ (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 × π 180 × r (when θ is in degrees)

Source: https://www.mathsisfun.com/geometry/circle-sector-segment.html