Question

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

15π2
Start Fraction 15 pi over 2 End Fraction

15π
15 pi

60π
60 pi

30π

Answer 1

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

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

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

Given:
- Radius \( r = 10 \) feet
- Central angle \( \theta = \frac{3\pi}{4} \)

Now, substituting the values into the formula:

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

Thus, the arc length is \(\frac{15\pi}{2}\).

The correct response is:

\[
\frac{15\pi}{2}
\]