(Sector of a Circle Calculator) A sector of a circle is a region bounded by two radii and an arc of the circle. It can be considered as a portion of the circle, like a slice of a pie.The size of the sector is determined by the central angle θ, which is the angle formed by the two radii at the center of the circle. The larger the central angle, the larger the sector.

Sector of a Circle Calculator

Sector of a Circle Calculator

Radius of Circle (r):

Central Angle (θ):



Area of Sector:

Arc Length:

The area of a sector can be calculated using the formula:

A = (θ/360) * π * r^2

where θ is the central angle in degrees, π is the mathematical constant pi (approximately equal to 3.14), and r is the radius of the circle.

The arc length of a sector can be calculated using the formula:

L = (θ/360) * 2 * π * r

where θ is the central angle in degrees, π is the mathematical constant pi (approximately equal to 3.14), and r is the radius of the circle.

Type of Sector of a Circle

There are two types of sectors of a circle:

1. Major sector: A major sector is a sector that has a central angle greater than 0 degrees and less than 180 degrees. It is also known as the larger sector.
2. Minor sector: A minor sector is a sector that has a central angle greater than 180 degrees. It is also known as the smaller sector.

Note: A semi-circle is a special type of sector where the central angle is equal to 180 degrees.

Example Sector of a Circle with solution

A sector of a circle is a portion of the circle enclosed by two radii and an arc. The formula to calculate the area of a sector is:

Area = (θ/360) * π * r^2

Where:

• θ is the central angle of the sector in degrees
• π is the mathematical constant pi (approx. 3.14)
• r is the radius of the circle

Here’s an example of how to calculate the area of a sector with a central angle of 60 degrees and a radius of 5 units:

θ = 60
r = 5

Area = (θ/360) * π * r^2
Area = (60/360) * π * 5^2
Area = (1/6) * π * 25
Area = (25/6) * π
Area = 25 * (π/6)
Area = 25 * (3.14/6)
Area = 25 * 0.52
Area = 13

So, the area of the sector is 13 square units.

frequently asked questions about sectors of a circle:

1. What is the formula to calculate the area of a sector?
2. How to find the central angle of a sector given its area and radius?
3. What is the relationship between the arc length of a sector and its central angle?
4. How to find the radius of a sector given its area and central angle?
5. What is the formula to calculate the length of an arc of a sector?
6. How to calculate the perimeter of a sector?
7. How to find the central angle of a sector given its arc length and radius?
8. What is the difference between a sector and a segment of a circle?
9. How to find the area of a sector given the arc length and radius?
10. What is the formula to calculate the arc length of a sector with a given central angle and radius?