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Area of a Sector of a Circle Formula
A circle is one of the most flawless forms in geometry. In geometry, the sector of a circle is the simplest shape.
It is a pie-shaped portion of a circle formed by its arc and two radii. A sector is produced when a segment of the circle’s circumference (also known as an arc) and two of its radii meet at both extremities of the arc. A sector of a circle has the appearance of a pizza slice or a pie. A sector is a segment of a circle that is characterised by the four characteristics listed below.
Two radii and an arc encompass a section of a circle.
A circle is split into two sectors, referred to as the minor sector and the major sector.
The larger section of the circle represents the main sector, while the smaller portion represents the minor sector.
In the case of semicircles, the circle is split into two sectors of equal size.
The intersection of the two radii at the portion of the circumference known as an arc forms a sector of a circle.
The section OAPB of the circle is known as the minor sector, while the section OAQB is known as the major sector.
The half-circle is also a sector with a 180-degree angle.
Area of a sector of a circle formula
The area of a sector of a circle is the quantity of space contained inside the sector’s perimeter. A sector always begins from the circle’s centre. The semicircle is likewise a sector of a circle, which in this instance has two equal-sized sectors. Let’s study how to determine the area of a sector. Given the radius of the circle (r) and the angle of the sector (θ), the formula for calculating the sector’s area is as follows:
Area of sector (A) = (θ/360°) × πr2
θ is the degree of the angle.
r is the radius.
Solved Examples
Example 1:Determine the area of the sector that is contained inside a circle whose radius is 20 units and whose arc length is 8 units.
Answer.
Provided in the question,
radius = 20 units and,
Length of the arc = 8 units
Area of sector of circle = (lr)/2
= (8 × 20)/2
= 80 sq. units.
