Question

If a central angle of 5π3 is created with two radii that are 30 inches long, then how long is the arc they will cut in radians?(1 point) Responses π2 Start Fraction pi over 2 End Fraction 15π 15 pi 50π 50 pi 5π18

Answer 1

To find the length of the arc created by a central angle in radians, you can use the formula:

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

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

In this case, the radius \( r \) is 30 inches and the angle \( \theta \) is \( \frac{5\pi}{3} \) radians.

Now, plug these values into the formula:

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

Calculating this:

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

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

So, the correct response is:

**50π**