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A circle sector is the region of a disk bounded by two radii and the arc between them. A slice cut radially from a round cake or an orange wedge has roughly the same shape.
A sector consists of three main components:
The two radii form a central angle at the center of the circle. For a fixed radius, this angle determines what fraction of the disk the sector occupies.
For a fixed radius, sector area is proportional to the central angle. Doubling the angle doubles the area of the corresponding sector.
The relationship between central angle and sector area can be expressed as a ratio. If the central angle is degrees, then the sector area is part of the total circle area.
For a fixed radius, sector area is proportional to the central angle. An angle of covers one-quarter of the circle, while covers one-half.
The area of a sector is determined by the circle radius and the central angle. The angle specifies what fraction of the full circle belongs to the sector.
Consider a circle with radius and a sector with central angle . Substitution gives:
The exact sector area is , approximately .
To understand the proportional relationship between central angle and sector area, look at various comparison examples:
A circle has a radius of . Determine the sector area formed by a central angle of .
A sector has area in a circle of radius . What is its central angle?
A round flatbread with diameter is cut radially through its center into equal sectors. Determine the area of each piece.
Solution Steps:
Given: ,
Solution Steps:
Given: sector area = ,
Solution Steps:
Given: diameter = , so The flatbread is cut radially into equal sectors, so the central angle of each piece is
Published: . Updated: .
