How to Calculate the Area of a Circle Sector

A circle sector is a portion of a circle enclosed by two radii and an arc. It looks like a slice of pizza or a pie. To find the area of a circle sector, you'll need to know the radius of the circle and the central angle of the sector.

Formula for Calculating the Area of a Circle Sector

The formula for calculating the area of a circle sector is:

Area of sector = (θ/360°) * πr²

Where:

• θ is the central angle of the sector in degrees
• r is the radius of the circle
• π is a mathematical constant, approximately equal to 3.14159

Steps to Calculate the Area of a Circle Sector

1. Identify the central angle (θ) and radius (r) of the sector.
2. Substitute the values of θ and r into the formula: Area of sector = (θ/360°) * πr²
3. Calculate the area.

Example

Let's say we have a circle sector with a central angle of 60 degrees and a radius of 5 cm. To find the area of this sector, we would follow these steps:

1. Identify the central angle (θ) and radius (r): θ = 60°, r = 5 cm
2. Substitute the values into the formula: Area of sector = (60°/360°) * π(5 cm)²
3. Calculate the area: Area of sector = (1/6) * π(25 cm²) ≈ 13.09 cm²

Practice Questions

Try these practice questions to test your understanding of calculating the area of a circle sector:

1. A circle sector has a central angle of 90 degrees and a radius of 8 cm. What is the area of the sector?
2. A circle sector has a central angle of 120 degrees and a radius of 10 cm. What is the area of the sector?

Key Points

• The area of a circle sector is a fraction of the total area of the circle.
• The fraction is determined by the ratio of the central angle of the sector to 360 degrees.
• Make sure the central angle is measured in degrees before using the formula.

Understanding how to calculate the area of a circle sector is an important skill in geometry. It has applications in various fields, such as engineering, architecture, and design.