If the radius of a circle is 10 feet and the central angle is 3π4 , then what is the arc length in radians?(1 point)

Responses

15π
15 pi

60π
60 pi

30π
30 pi

15π2

1 answer

To find the arc length of a circle, you can use the formula:

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

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

In this case, the radius \( r \) is 10 feet, and the central angle \( \theta \) is \( \frac{3\pi}{4} \) radians.

Plugging in the values into the formula:

\[ \text{Arc Length} = 10 \times \frac{3\pi}{4} = \frac{30\pi}{4} = \frac{15\pi}{2} \]

Therefore, the arc length is \( \frac{15\pi}{2} \). However, since the options provided do not contain \( \frac{15\pi}{2} \), we should check for simplifications.

None of the options given are correct based on the calculations. If you need to choose from the provided options, please confirm if the arc length formula or angle is given correctly.