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

15π
15 pi

π2
Start Fraction pi over 2 End Fraction

5π18
Start Fraction 5 pi over 18 End Fraction

Answer 1

To find the length of the arc (s) created by a central angle (θ) in radians with a radius (r), you can use the formula:

\[ s = r \cdot θ \]

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

Now, substitute the values into the formula:

\[ s = 30 \cdot \frac{5\pi}{3} \]

Calculating this gives:

\[ s = 30 \cdot \frac{5}{3} \cdot \pi = 10 \cdot 5\pi = 50\pi \]

So, the length of the arc is:

**50π**.