Last updated on August 5th, 2025
In geometry, the area of a sector refers to a portion of a circle enclosed by two radii and the corresponding arc. This topic will cover the formula used to calculate the area of a sector in a circle for class 10 students.
The area of a sector is a part of a circle's area, calculated using specific formulas. Let’s learn the formula to calculate the area of a sector.
The area of a sector is determined by the angle of the sector (θ) and the radius (r) of the circle. It is calculated using the formula:
Area of a sector = (θ/360) × πr², where θ is the angle in degrees.
In geometry and real life, the formula for the area of a sector is crucial for calculating portions of circular regions. Here are some reasons why it's important:
- It helps in determining the area of circular segments in various fields such as architecture and engineering.
- Understanding this formula allows students to solve problems related to circle geometry efficiently.
- It is foundational for advanced topics in mathematics, including calculus and trigonometry.
Students often find math formulas challenging. Here are some tips to master the area of a sector formula:
- Remember that the formula is a fraction of the circle's area, which is πr², scaled by the angle θ/360.
- Visualize the sector as a "pizza slice" of the circle to better understand the concept.
- Practice by applying the formula to real-world problems, such as finding the area of pie slices or circular plots.
The area of a sector formula is used in various real-life scenarios. Here are some applications:
- In architecture, to calculate the area of curved surfaces or domes.
- In agriculture, to determine the area of circular sections of farmland.
- In design, for creating circular patterns or segments in graphics and art.
Students often make errors when calculating the area of a sector. Here are some common mistakes and ways to avoid them:
Find the area of a sector with a radius of 10 cm and an angle of 90 degrees.
The area of the sector is 78.5 cm²
To find the area of the sector, use the formula:
Area = (θ/360) × πr² = (90/360) × π × 10² = 1/4 × π × 100 = 25π
Thus, the area is approximately 78.5 cm².
A circle has a radius of 5 meters, and the sector has an angle of 60 degrees. Find the area of the sector.
The area of the sector is 13.09 m²
Use the formula for the area of a sector:
Area = (θ/360) × πr² = (60/360) × π × 5² = 1/6 × π × 25
The area is approximately 13.09 m².
Calculate the area of a sector with a radius of 8 inches and an angle of 45 degrees.
The area of the sector is 25.13 in²
Using the formula:
Area = (θ/360) × πr² = (45/360) × π × 8² = 1/8 × π × 64
The area is approximately 25.13 in².
Determine the area of a sector with a 12 cm radius and a 150-degree angle.
The area of the sector is 75.4 cm²
Apply the formula:
Area = (θ/360) × πr² = (150/360) × π × 12² = 5/12 × π × 144
The area is approximately 75.4 cm².
A sector of a circle has a radius of 7 cm and an angle of 30 degrees. Find its area.
The area of the sector is 12.83 cm²
Using the formula:
Area = (θ/360) × πr² = (30/360) × π × 7² = 1/12 × π × 49
The area is approximately 12.83 cm².
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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