EDEXCEL GCSE FOUNDATION MATHS - What is the Arc Length

Edexcel GCSE Foundation Maths: What is the Arc Length?

Introduction

The arc length is the distance along the curved edge of a circle or part of a circle (a sector). It's like the length of a piece of string that would fit perfectly along that curved edge.

Formula

The formula for calculating arc length is:

Arc Length = (Angle/360) x 2?r

Where:

• Angle is the central angle of the sector (in degrees)
• ? (pi) is a mathematical constant approximately equal to 3.14159
• r is the radius of the circle

Example 1:

Problem: Find the arc length of a sector with a central angle of 60° and a radius of 5 cm.

Solution:

1. Substitute the values into the formula: Arc Length = (60/360) x 2 x 3.14159 x 5
2. Simplify: Arc Length = (1/6) x 31.4159
3. Calculate: Arc Length = 5.236 cm (approximately)

Therefore, the arc length of the sector is approximately 5.236 cm.

Example 2:

Problem: A sector of a circle has an arc length of 10 cm and a central angle of 90°. Find the radius of the circle.

Solution:

1. Substitute the values into the formula: 10 = (90/360) x 2 x 3.14159 x r
2. Simplify: 10 = (1/4) x 6.28318 x r
3. Solve for r: r = (10 x 4) / (6.28318) r = 6.366 cm (approximately)

Therefore, the radius of the circle is approximately 6.366 cm.

Key Points

• The arc length is always measured in units of length (e.g., cm, m, km).
• The angle must be in degrees.
• Make sure you are working with the correct radius of the circle.
• If you are given the arc length and the radius, you can use the formula to find the central angle.

Practice

Try practicing with different problems by varying the angle and radius and calculating the arc length. You can also try working backward from the arc length and radius to find the angle.