Length of an Arc
(KS3, Year 7)
How to Find the Length of an Arc of a Circle
Finding the length of an arc of a circle is easy.Question
What is the length of the arc with an angle of 60° and a radius of 5 cm, as shown below?Step-by-Step:
1
Start with the formula:
Length of arc = θ⁄360° × 2πr
Don't forget: π is pi (≈ 3.14) and / means ÷.
2
Substitute the angle and the radius into the formula. In our example, θ = 60° and r = 5.
Length of arc = 60°⁄360° × 2 × π × 5
Length of arc = (60° ÷ 360°) × 2 × 5 × π
Length of arc = 5.2 cm
Answer:
The length of an arc of a circle with a radius of 5 cm, which is subtended by an angle of 60°, is 5.3 cm.What Is an Arc?
An arc is a portion of the circumference.Why Does the Formula Work?
The length of an arc is just a fraction of the circumference of the circle of the same radius. The circumference is given by 2πr, where r is the radius. For example, an arc that is halfway round a circle is half the circumference of a circle. An arc that is a quarter way round a circle is quarter the circumference of a circle. In each case, the fraction is the angle of the arc divided by the full angle of the circle. When measured in degrees, the full angle is 360°. Hence for a general angle θ, the formula is the fraction of the angle θ over the full angle 360° multiplied by the circumferece of the circle:
Length of arc = θ⁄360° × 2πr
Beware
Is the Angle Given in Degrees or Radians
The formula to find the length of an arc of a circle depends on whether the angle at the center of the arc is given in degrees or radians. Make sure you check what units the angle is given in.Worksheet
This test is printable and sendable