Question

type the correct answer in the box. use numerals instead of words. an arc of circle m has length 32π centimeters and the corresponding central angle has a radian measure of 8/9 π. what is the radius of the circle? the radius of the circle is centimeters. reset next

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc \( s \) in a circle with radius \( r \) and central angle \( \theta \) (in radians) is \( s = r\theta \).

Step2: Substitute known values

We know \( s = 32\pi \) and \( \theta=\frac{8}{9}\pi \). Substituting into the formula: \( 32\pi = r\times\frac{8}{9}\pi \).

Step3: Solve for \( r \)

First, divide both sides by \( \pi \): \( 32 = r\times\frac{8}{9} \). Then, multiply both sides by \( \frac{9}{8} \): \( r = 32\times\frac{9}{8} \). Calculating \( 32\times\frac{9}{8} = 4\times9 = 36 \).

Answer:

36