Question

the radius of a circle is 15 kilometers. what is the length of a 180° arc?
180°
r=15 km
give the exact answer in simplest form.
kilometers
π

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 \( r = 15 \) km. Substitute these into the formula:
\( L=\frac{180^\circ}{360^\circ}\times2\pi\times15 \)
Simplify \( \frac{180^\circ}{360^\circ}=\frac{1}{2} \), so \( L=\frac{1}{2}\times2\pi\times15 \)
The \( 2 \) in the numerator and denominator cancels out, leaving \( L = 15\pi \)

Answer:

\( 15\pi \)