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

30π
30 pi

15π2
Start Fraction 15 pi over 2 End Fraction

60π
60 pi

15π

Answer 1

To find the arc length \( L \) of a circle given the radius \( r \) and the central angle \( \theta \) in radians, you can use the formula:

\[
L = r \cdot \theta
\]

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

Now, plug the values into the formula:

\[
L = 10 \cdot \frac{3\pi}{4} = \frac{30\pi}{4} = \frac{15\pi}{2}
\]

Therefore, the arc length is:

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

So the correct response is \( \frac{15\pi}{2} \) (15π/2).