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

9π
9 pi

18π
18 pi

141π2
Start Fraction 141 pi over 2 End Fraction

π18

Answer 1

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

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

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

1. **Find the radius**: Given that the diameter of the circle is 94 kilometers, the radius \( r \) can be calculated as follows:
\[
r = \frac{\text{Diameter}}{2} = \frac{94}{2} = 47 \text{ kilometers}
\]

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

3. **Calculate the arc length**:
\[
\text{Arc Length} = r \theta = 47 \times \frac{3\pi}{2}
\]
\[
\text{Arc Length} = 47 \times 3\pi / 2 = \frac{141\pi}{2} \text{ kilometers}
\]

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

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

The correct response is:

**141π/2**