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. 18π cm b. 32π cm c. 5.625 cm d. 216π cm

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( L = \frac{\theta}{360^\circ} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Substitute given values

Here, \( \theta = 135^\circ \) and \( r = 24 \) cm. Substitute these into the formula:
\( L = \frac{135^\circ}{360^\circ} \times 2\pi \times 24 \)

Step3: Simplify the expression

First, simplify \( \frac{135}{360} = \frac{3}{8} \). Then:
\( L = \frac{3}{8} \times 48\pi \) (since \( 2\times24 = 48 \))
\( L = 3\times6\pi = 18\pi \)

Answer:

A. \( 18\pi \) cm