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

141π2
Start Fraction 141 pi over 2 End Fraction

9π
9 pi

π18
Start Fraction pi over 18 End Fraction

18π

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 angle in radians.

First, let's find the radius of the circle. The diameter of the circle is given as 94 kilometers, so the radius \( r \) is half of that:

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

Next, we know the central angle \( \theta = \frac{3\pi}{2} \) radians.

Now plug these values into the arc length formula:

\[
\text{Arc length} = r \theta = 47 \times \frac{3\pi}{2}
\]

Calculating this:

\[
\text{Arc length} = 47 \times \frac{3\pi}{2} = \frac{141\pi}{2}
\]

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

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