Examples on Areas of Sector and Segment of a Circle

Example 1: Find the area of the sector given that radius of circle is 4 cm and angle subtended by sector is π/3 radians.

Solution:

To find area of sector we use following formula

Area of Sector = (1/2) × θr²

Area of Sector = (1/2) × (π/3)4²

Area of Sector = 8 × (π/3)

Area of Sector = 8.38 cm²

Example 2: Determine the area of segment given the radius of the circle is 2 cm and angle subtended by segment is 90°.

Solution:

To find area of segment we use following formula

Area of Segment (when θ is in degrees) = (1/2) × r²[(π/180)θ – sinθ]

Area of Segment = (1/2) × 2²[(π/180°)90° – sin90°]

Area of Segment = (1/2) × 4[(π/2) – 1]

Area of Segment = 2 × [(π/2) – 1]

Area of Segment = 1.142 cm²

Example 3: Find the area of the major segment if the area of minor segment is 4 cm² and area of circle is 10 cm².

Solution:

To find area of major segment we use formula

Area of Major Segment = Area of Circle – Area of Minor Segment

Area of Major Segment = 10 – 4

Area of Major Segment = 6 cm²

Example 4: Determine the area of the minor sector if the area of major sector is 110 cm² and area of circle is 200 cm².

Soliution:

To find area of minor sector we use formula

Area of Major Sector = Area of Circle – Area of Minor Sector

Area of Minor Sector = 200 – 110

Area of Minor Sector = 90 cm²

Areas of sector and segment of a circle with radius r and subtends an angle θ (in radians) are given by (1/2)×θr² and (1/2)×r²(θ -sinθ) respectively. The area of the sector and the area of the segment of the circle are easily calculated using the above formula.

In this article, we will explore the areas of sector and segment in detail and also learn the basics of sector and segment of a circle.