Question

the diameter of a circle is 18 inches. what is the length of a 120° arc?
120°
d=18 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 \( d = 18 \) inches, so \( C=\pi\times18 = 18\pi \) inches.

Step2: Determine the fraction of the circle the arc represents

The central angle of the arc is \( 120^\circ \), and a full circle is \( 360^\circ \). So the fraction is \( \frac{120^\circ}{360^\circ}=\frac{1}{3} \).

Step3: Calculate the arc length

Multiply the circumference by the fraction: Arc length \( = 18\pi\times\frac{1}{3}=6\pi \) inches.

Answer:

\( 6\pi \)