Question

a circle has a radius of 18 cm. what is the length of an arc that has a measure of 90°? a 9π cm b 10π cm c 28π cm d 14π cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. First, convert the angle from degrees to radians. We know that $90^{\circ}=\frac{\pi}{2}$ radians, and $r = 18$ cm.

Step2: Substitute values into formula

Substitute $r = 18$ and $\theta=\frac{\pi}{2}$ into the formula $s=r\theta$. So $s=18\times\frac{\pi}{2}$.

Step3: Calculate the arc - length

$18\times\frac{\pi}{2}=\frac{18\pi}{2}=9\pi$ cm.

Answer:

A. $9\pi$ cm