Sectors of a Circle
What are Sectors of a Circle?
The sectors of a circle are parts or portions of the circle that are bounded by two radii and the corresponding arc between them.
What is a Central Angle in a Circle Sector?
A central angle is an angle with its vertex at the centre of a circle and its sides extending to the endpoints of an arc. It determines the size of the sector and is measured in degrees or radians.
How is Area of a Sector of a Circle Calculated?
The area of a sector can be calculated using the formula as follows:
Area of Sector = (θ/360) × πr2
Where,
- θ is the measure of the central angle in degrees,
- π is a mathematical constant (π≈3.14), and
- r is the radius of the circle.
What is Arc Length of a Sector?
The arc length of a sector is the distance along the circumference of the circle that forms the arc.
What is the formula for Arc length of a Sector?
Arc length of a sector is given by the following formula:
Arc Length of Sector = (θ/360) × 2πr
Where,
- θ is the measure of the central angle in degrees,
- π is a mathematical constant (π≈3.14), and
- r is the radius of the circle.
How is Perimeter of a Circle’s Sector Calculated?
The perimeter of a circle sector is the sum of the length of the arc and the lengths of the two radii that form the sector. The formula for the perimeter of a circle is given by:
- Perimeter of Sector = Arc Length + 2 × r
- Perimeter of Sector = (θ/360) × 2πr + 2 × r
Where,
- θ is the measure of the central angle in degrees,
- π is a mathematical constant (π≈3.14), and
- r is the radius of the circle.
Can Area of Sector be Larger than Area of Whole Circle?
No, the area of any sector can’t be larger than the area of the whole circle as it is the part of the circle and it can maximum be equal to the area of a circle as the largest possible sector is a full circle.
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