What is Sector of a Circle?
A sector is a segment of a circle that includes an arc and the two radii that connect the arc’s endpoints to the circle’s centre. It represents a fraction of the circle, defined by the arc—part of the circle’s perimeter—and the radii at the arc’s ends. Visually, a sector resembles a piece of pizza or pie, highlighting its nature as a portion of the whole circle.
Sector of a Circle Definition
A sector of a circle is a portion of a circle that is enclosed by two radii and the arc that they form.
In other words, a sector of a circle is a pie-shaped section of a circle formed by the arc and its two radii and it is produced when a section of the circle’s circumference (also known as an arc) and two radii meet at both extremities of the arc. A semi-circle, which represents half of a circle, is the most frequent sector of a circle.
We can see in the above illustrated diagram, that there are two sectors formed in the circle always.
- Major Sector: The sector with a larger arc length is called the major sector.
- Minor Sector: The sector with a smaller arc length is called the minor sector.
Sector Angle
The angle subtended by the arc at the centre of the circle is known as the sector angle or central angle of the sector. In the above diagram, we can see that, the angle subtended by the minor sector is θ, thus θ is the sector angle for the minor sector. As we know total angle subtended at any point is 360°, thus the angle subtended by the major sector is 360° – θ.
Sector of a Circle
Sector of a Circle is one of the components of a circle like a segment which students learn in their academic years as it is one of the important geometric shapes. The sector of a circle is a section of a circle formed by the arc and its two radii and it is produced when a section of the circle’s circumference and two radii meet at both extremities of the arc. From a slice of pizza to a region between two fan blades, we can see sectors of the circle in our daily lives everywhere.
In this article, we will explore the geometric shape of the sector which is derived from the circle in detail including its areas, perimeter, and all the formulas related to the sector of a circle.
Table of Content
- What is Sector of a Circle?
- Sector of a Circle Definition
- Sector Angle
- Sector of a Circle Examples
- Sector of a Circle Area
- Formula for Area of a Sector
- Derivation of Formula for Area of a Sector
- Area of Minor Sector
- Area of Major Sector
- Arc Length of Sector of a Circle
- Formula for Arc Length of a Sector
- Derivation of Formula for Arc Length of a Sector
- Sector of a Circle Perimeter
- Perimeter of a Sector Formula
- Sample Problems Sector of a Circle
- Summarizing Important Formulas of Sector of a Circle