Length of an Arc (Radians)
(KS3, Year 7)
How to Find the Length of an Arc of a Circle (Radians)
Finding the length of an arc of a circle, when the angle is in radians, is easy.Question
What is the length of the arc with an angle of 1 radian and a radius of 5 cm, as shown below?Step-by-Step:
1
Start with the formula:
Length of arc = rθ
2
Substitute the radius and the angle into the formula. In our example, r = 5 and θ = 1.
Length of arc = 5 × 1
Length of arc = 5 cm
Answer:
The length of an arc of a circle with a radius of 5 cm, which is subtended by an angle of 1 radian, is 5 cm.What Is an Arc?
An arc is a portion of the circumference.What Are Radians?
Radians are a way of measuring angles. 1 radian is the angle found when the radius is wrapped around the circle.Why Does the Formula Work?
An angle in radians can be found using the formula:
Angle = Arc length ⁄ Radius
We can rearrange this formula to make the arc length the subject:
Arc length = Angle × Radius
Arc length = θ × r
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