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 × r² × 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 cm²

Example 3: For a circle of a given area 50cm², there are three sectors of area 25cm², 45cm², and 13cm². Classify the given sectors among the minor sector, semi-circle, and major sector.

Solution:

Area of the circle is 50cm².

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 360^o.

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

So, area of each sector is given by,

Area of Each Slice = (θ / 360°) × πr²,

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

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.