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
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.
Table of Content
- What is Sector and Segment of a Circle?
- Areas of Sector and Segment of a Circle
- Examples on Areas of Sector and Segment of a Circle
- Practice Problems on Areas of Sector and Segment of a Circle
- FAQs on Areas of Segment and Sector of a Circle