Question

the diameter of a circle is 18 centimeters. what is the length of a 30° arc?

d=18 cm

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 \( d = 18 \) cm, so \( C = \pi \times 18 = 18\pi \) cm.

Step2: Calculate the fraction of the circle the arc represents

A full circle is \( 360^\circ \), and the arc is \( 30^\circ \). The fraction is \( \frac{30^\circ}{360^\circ} = \frac{1}{12} \).

Step3: Find the length of the arc

Multiply the circumference by the fraction: \( \text{Arc Length} = 18\pi \times \frac{1}{12} = \frac{18\pi}{12} = \frac{3\pi}{2} \) cm.

Answer:

\(\frac{3}{2}\pi\) (or \(1.5\pi\), but \(\frac{3}{2}\pi\) is in simplest exact form)