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

1 answer

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 central angle \( \theta \) is \( \frac{5\pi}{3} \) radians.

Now, substitute the values into the formula:

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

Calculating this:

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

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

The correct response is:

50π