Question

the diameter of a circle is 6 inches. what is the length of a 90° arc?
90°
d=6 in
give the exact answer in simplest form.
inches
π
\frac{□}{□}

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 \( d = 6 \) inches, so \( C = \pi \times 6 = 6\pi \) 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: \( \text{Arc Length} = 6\pi \times \frac{1}{4} = \frac{6\pi}{4} = \frac{3\pi}{2} \).

Answer:

\(\frac{3}{2}\pi\) (or \( \frac{3\pi}{2} \))