Question

If a circle has a diameter of 94 kilometers and a central angle of 3π2
, then what is the length of the arc created by the angle?(1 point)
Responses

π18
Start Fraction pi over 18 End Fraction

9π
9 pi

18π
18 pi

141π2

Answer 1

To find the length of the arc created by a central angle in a circle, you can use the formula:

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

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

1. **Find the radius:** The diameter is given as 94 kilometers, so the radius \( r \) is:

\[
r = \frac{diameter}{2} = \frac{94}{2} = 47 \text{ kilometers}
\]

2. **Use the central angle:** The central angle is \( \frac{3\pi}{2} \) radians.

3. **Calculate the arc length:**

\[
\text{Arc Length} = r \cdot \theta = 47 \cdot \frac{3\pi}{2}
\]

4. **Perform the multiplication:**

\[
\text{Arc Length} = 47 \cdot \frac{3\pi}{2} = \frac{141\pi}{2}
\]

So, the length of the arc created by the angle is:

\[
\frac{141\pi}{2}
\]

Among the provided options, the correct answer looks like:

\[
\frac{141\pi}{2}
\]

Therefore, the correct response is:

\(\mathbf{141\pi/2}\)