How to Calculate Area of Sector of Circle? (original) (raw)

Last Updated : 27 Apr, 2024

Area of the sector is easily calculated by using various formulas of geometry. In this article, we have covered a definition of sector circles, types of sectors, and others in detail.

Table of Content

Sector Definition

Sector is defined as the portion inside a circle bounded between two radii and the arc of the circle. The area of this sector depends upon the corresponding angle between the two radii. The image of the sector of the circle is shown below:

Major-and-Minor-Sector

Sector Definition

**Properties of Sector

**Types of Sectors

There are three types of sectors depending upon the angle between the corresponding two radii of the sector. They are:

**Formula for Area of a Sector

For a circle having radius equals to 'r' units and angle of the sector is θ ****(in degrees)**, the area is given by,

**Area of sector = θ / 360° × πr 2

When **θ is given in **radian, the area is given by

**Area of sector = 1/2 × r 2 θ

**Proof:

For a circle with radius r units, the area is given by **πr 2 .

Now the fraction of the area enclosed by the sector will be the same as the fraction of the angle enclosed by the sector in the circle.

Thus, the fraction of area enclosed = θ / 360°

So, the area enclosed by the sector = ****(θ / 360°) × πr** 2

**Examples on Area of Sector of Circle

**Example 1: Find the area of the sector of a **circle whose angle enclosed equals 60 o and the radius of the **circle is 5 units. It is a **major or minor sector?

**Solution:

Give, the angle of the sector = θ = 60**°

Radius of the circle = 5 units

Thus, aea of the sector = 60°/360° × π × 52 = 25π/6

Approximating the value of π = 3.14, we get,

Area of sector = 25 × 3.14 / 6 = 13.08 sq. units

**Since, angle of sector is less than 180°, it is a minor sector.

**Example 2: Find the area of a sector whose angle is given as π/2 radians and the radii of the circle is 8cm.

**Solution:

Since angle of the sector is given in radian, we can write,

**Area of the sector = 1/2 × r 2 × θ

Given, radius of circle is 8cm. Thus,

Area of Sector = 1/2 × 82 × π/2 = 16π cm2

Approximating Value of π = 3.14, we get,

Area of sector = 16 × 3.14 = **50.24 cm 2

**Example 3: For a circle of a given area 50cm 2 , there are three sectors of area 25cm 2 , 45cm 2 , and 13cm 2 . Classify the given sectors among the minor sector, semi-circle, and major sector.

**Solution:

Area of the circle is 50cm 2 .

Thus, half of the area of the circle is 50/2 = 25cm2.

Thus, sector with an area of 25cm2 is a **semi-circle.

Sector with an area of 45cm2 has a greater area than a semi-circle. Thus, it is a major sector.

Lastly, sector with an area of 13cm2 has a smaller area than a semi-circle. Thus, it is a **minor sector.

**Example 4: If a pizza of radius 5 inches is divided into 6 equal slices, find the area enclosed and angle of each slice of pizza.

**Solution:

Since we divide a pizza into 6 equal pieces, each piece represents a sector with an angle equal to one-sixth of the total angle of pizza, that is 360o.

So, angle of each pizza slice = 360**°/6 = **60°.

So, area of each sector is given by,

**Area of Each Slice = (θ / 360°) × πr 2,

where,

θ = 60**°

r = 5 inches

Thus, we get, area of each slice = 60°/360° × π × 52 = 25π/6 sq. inch

Putting the value of π = 3.14, we get

**Area of Each Slice = 25 × 3.14 / 6 = 13.08 sq. inch