Question

In a circle whose radius is 4 centimeters, what is the length, in centimeters, of an arc intercepted by a central angle of 2 1/2 radians?

Answer 1

The circumference of a cirdcle is

\( C = 2 \pi r \)

This is based on the entire circle being an angle of \(2 \pi\) radians.

For the length of an arc of a circle with a central angle of \( \theta\), the angle is the following fraction of the the circle \(\dfrac{\theta}{2 \pi} \).

The length of an arc with cetral angle of \( \theta\) is

\(s = \dfrac{\theta}{2 \pi} \times 2 \pi r = r \theta \)

All you need to do is use the formula:

\(s = r \theta \)

where s = arc length,
r = radius,
\(\theta\) = central angle.