Question

the diameter of a circle is 2 miles. what is the length of a 180° arc?
d=2 mi
180°
give the exact answer in simplest form.
miles

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( s=\frac{\theta}{360^\circ}\times C \), where \( \theta \) is the central angle in degrees and \( C \) is the circumference of the circle. The circumference of a circle is \( C = \pi d \) (where \( d \) is the diameter).

Step2: Calculate the circumference

Given \( d = 2 \) miles, the circumference \( C=\pi\times2 = 2\pi \) miles.

Step3: Calculate the arc length

The central angle \( \theta = 180^\circ \). Substitute into the arc length formula: \( s=\frac{180^\circ}{360^\circ}\times2\pi \). Simplify \( \frac{180^\circ}{360^\circ}=\frac{1}{2} \), so \( s=\frac{1}{2}\times2\pi=\pi \).

Answer:

\(\pi\)