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 5π18 Start Fraction 5 pi over 18 End Fraction 50π 50 pi 15π 15 pi π2

Answer 1

To find the length of the arc (s) that corresponds to a central angle (θ) in radians, we use the formula:

\[ s = r \times \theta \]

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

Given that the radius \( r = 30 \) inches and the central angle \( θ = \frac{5\pi}{3} \), we can substitute these values into the formula:

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

Now, perform the multiplication:

\[ s = 30 \times \frac{5\pi}{3} = \frac{30 \times 5\pi}{3} = \frac{150\pi}{3} = 50\pi \]

Therefore, the length of the arc is:

\[ \boxed{50\pi} \]