Question

the diameter of a circle is 8 inches. what is the length of a 45° arc?
d=8 in
give the exact answer in simplest form.
inches

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 \( d = 8 \) inches, so \( C=\pi\times8 = 8\pi \) inches.

Step2: Determine the fraction of the circle the arc represents

The central angle of the arc is \( 45^\circ \), and a full circle is \( 360^\circ \). The fraction of the circle the arc is, is \( \frac{45}{360}=\frac{1}{8} \).

Step3: Calculate the arc length

Arc length is the fraction of the circumference. So arc length \( = \frac{1}{8}\times8\pi=\pi \) inches.

Answer:

\(\pi\)