How to Calculate the Length of an Arc in a Circle

What is the formula for finding the length of an arc in a circle?

Is it possible to calculate the length of an arc in a circle if we know the radius and central angle?

Formula for Finding the Length of an Arc in a Circle

Yes, you can calculate the length of an arc in a circle if you know the radius and central angle. The formula to find the length of an arc in a circle is:

S = rθ

To calculate the length of an arc in a circle, we can use the formula S = rθ, where S represents the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

By substituting the given values of the radius and central angle into the formula, we can find the length of the arc.

For example, if the radius of a circle is 10 inches and the central angle is π/3 radians, we can calculate the length of the arc as follows:

S = 10 inches x π/3 radians = 10π/3 inches ≈ 10.47 inches

Therefore, the approximate length of the arc intersected by a central angle of π/3 radians in a circle with a radius of 10 inches is approximately 10.47 inches.