Question

the diameter of a circle is 6 miles. what is the length of a 135° arc?
d=6 mi
135°
give the exact answer in simplest form.
miles

Explanation:

Step1: Find the circumference of the circle

The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter. Given \( d = 6 \) miles, so \( C=\pi\times6 = 6\pi \) miles.

Step2: Determine the fraction of the circle the arc represents

The central angle of the arc is \( 135^\circ \), and a full circle is \( 360^\circ \). The fraction is \( \frac{135}{360}=\frac{3}{8} \).

Step3: Calculate the arc length

Multiply the circumference by the fraction: Arc length \(=\frac{3}{8}\times6\pi=\frac{18\pi}{8}=\frac{9\pi}{4} \) miles.

Answer:

\(\frac{9}{4}\pi\) (or \( \frac{9\pi}{4} \))