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

15π
15 pi

30π
30 pi

15π2
Start Fraction 15 pi over 2 End Fraction

60π
60 pi

Answer 1

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

\[
L = r \theta
\]

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

In your case:
- The radius \( r = 10 \) feet.
- The central angle \( \theta = \frac{3\pi}{4} \) radians.

Now, substituting the values into the formula:

\[
L = 10 \times \frac{3\pi}{4}
\]

Calculating this, we get:

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

Therefore, the arc length is:

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

So, the correct response from the options given is:

**Start Fraction 15 pi over 2 End Fraction (15π/2)**.