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

15π
15 pi

60π

Answer 1

To find the arc length of a circle, 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 10 feet, and the central angle \( \theta \) is \( \frac{3\pi}{4} \) radians.

Now, substitute the values into the formula:

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

Calculating this gives:

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

So, the arc length is:

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

The correct response is **Start Fraction 15 pi over 2 End Fraction**.