Question

select the correct answer. arc cd located on circle a has a central angle of 135°. the radius of the circle is 24 centimeters. what is the length of arc cd? a. 5.625 cm b. 18π cm c. 32π cm d. 216π cm

Explanation:

Step1: Recall arc length formula

The formula for arc length is $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle, and $r$ is the radius.

Step2: Substitute given values

$\theta = 135^\circ$, $r = 24$ cm.
$L = \frac{135^\circ}{360^\circ} \times 2\pi \times 24$

Step3: Simplify the expression

First, $\frac{135}{360} = \frac{3}{8}$. Then:
$L = \frac{3}{8} \times 48\pi = 18\pi$

Answer:

B. $18\pi$ cm