Question

the diameter of a circle is 8 centimeters. what is the length of a 135° arc?
d=8 cm
135°
give the exact answer in simplest form.
centimeters

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

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 \(=\frac{3}{8}\times8\pi = 3\pi \) cm.

Answer:

\( 3\pi \)