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

50π
50 pi

5π18
Start Fraction 5 pi over 18 End Fraction

15π
15 pi

π2

Answer 1

To find the length of the arc that a central angle subtends in a circle, we can use the formula:

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

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

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

Now, substituting the values into the formula:

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

To simplify:

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

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

The correct answer is:

**50π**