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

1 answer

To find the length of the arc (L) formed by a central angle in a circle, we can use the formula:

\[ L = r \times \theta \]

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

Given:

  • \( r = 30 \) inches
  • \( \theta = \frac{5\pi}{3} \) radians

Now we can substitute these values into the formula:

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

Calculating this:

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

Thus, the length of the arc is:

\[ \boxed{50\pi} \]