Question

the radius of a circle is 6 inches. what is the length of a 150° arc?
give the exact answer in simplest form.
inches

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( L=\frac{\theta}{360^\circ}\times2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Substitute values

Given \( \theta = 150^\circ \) and \( r = 6 \) inches. Substitute these into the formula:
\( L=\frac{150^\circ}{360^\circ}\times2\pi\times6 \)
Simplify the fraction \( \frac{150}{360}=\frac{5}{12} \), and \( 2\times6 = 12 \). So we have \( L=\frac{5}{12}\times12\pi \)

Step3: Simplify the expression

The 12 in the numerator and denominator cancels out, leaving \( L = 5\pi \)

Answer:

\( 5\pi \)