Question

the diameter of a circle is 18 inches. what is the length of a 90° arc?
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

A full circle is \( 360^\circ \), and the arc is \( 90^\circ \). The fraction is \( \frac{90^\circ}{360^\circ}=\frac{1}{4} \).

Step3: Calculate the arc length

Multiply the circumference by the fraction: \( \text{Arc Length}=\frac{1}{4}\times18\pi=\frac{9}{2}\pi \) inches.

Answer:

\( \frac{9}{2}\pi \)