Question

the radius of a circle is 3 kilometers. what is the length of a 180° arc?
give the exact answer in simplest form.
kilometers

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( L=\frac{\theta}{360^{\circ}}\times2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Substitute values

Given \( \theta = 180^{\circ} \) and \( r = 3 \) kilometers. Substitute these values into the formula:
\( L=\frac{180^{\circ}}{360^{\circ}}\times2\pi\times3 \)
Simplify \( \frac{180^{\circ}}{360^{\circ}}=\frac{1}{2} \), so the expression becomes \( \frac{1}{2}\times2\pi\times3 \).
The \( 2 \) in the numerator and the \( 2 \) in the denominator cancel out, leaving \( \pi\times3 = 3\pi \).

Answer:

\( 3\pi \)