Question

If a central angle of 5π/3 is created with two radii that are 30 inches long, then how long is the arc they will cut in radians?

a. π/2
b. 5π/18
c. 15π
d. 50π

Answer 1

To find the length of the arc that is cut by the central angle, you can use the formula:

\[
\text{Arc Length} = r \theta
\]

where \( r \) is the radius and \( \theta \) is the central angle in radians.

In this case:

- The radius \( r = 30 \) inches
- The central angle \( \theta = \frac{5\pi}{3} \) radians

Now plug these values into the formula:

\[
\text{Arc Length} = 30 \times \frac{5\pi}{3}
\]

Calculate the expression:

\[
\text{Arc Length} = 30 \times \frac{5\pi}{3} = 10 \times 5\pi = 50\pi \text{ inches}
\]

So, the length of the arc is \( 50\pi \) inches.

Therefore, the answer is:

\[
\text{d. } 50\pi
\]