To find the length of the arc created by a central angle in a circle, you can use the formula:
\[ \text{Arc Length} = \frac{\theta}{2\pi} \times C \]
where \(\theta\) is the central angle in radians, and \(C\) is the circumference of the circle.
First, we need to calculate the circumference of the circle. The formula for circumference \(C\) is:
\[ C = \pi d \]
where \(d\) is the diameter. Given that the diameter \(d\) is 94 kilometers:
\[ C = \pi \times 94 = 94\pi \text{ kilometers} \]
Now, we have a central angle \(\theta = \frac{3\pi}{2}\) radians. Now, substituting these values into the arc length formula:
\[ \text{Arc Length} = \frac{\frac{3\pi}{2}}{2\pi} \times 94\pi \]
Simplifying the fraction:
\[ \text{Arc Length} = \frac{3}{4} \times 94\pi \]
Now, calculate \( \frac{3 \times 94}{4} \):
\[ 3 \times 94 = 282 \] \[ \frac{282}{4} = 70.5 \]
So, the arc length will be:
\[ \text{Arc Length} = 70.5\pi \text{ kilometers} \]
Since none of the response options match \(70.5\pi\), let's convert \(70.5\) into a fraction, which is:
\[ 70.5\pi = \frac{141}{2}\pi \]
Thus, the final arc length in the given response options corresponds to 141π/2.
Therefore, the answer is:
141π/2.
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