Question

question 1 (multiple choice worth 1 points)
(07.03r mc)
a ferris wheel car moves from point c to point d on the circle shown below:
what is the arc length the car traveled, to the nearest hundredth?
7.91 feet
8.32 feet
10.99 feet
11.89 feet

Explanation:

Step1: Find the radius

The diameter $d = 30$ ft, so the radius $r=\frac{d}{2}=\frac{30}{2}=15$ ft.

Step2: Use the arc - length formula

The formula for arc length $s$ of a circle is $s = r\theta$ (where $\theta$ is in radians). First, convert the angle from degrees to radians. We know that $42^{\circ}=42\times\frac{\pi}{180}=\frac{7\pi}{30}$ radians. Then, substitute $r = 15$ and $\theta=\frac{7\pi}{30}$ into the arc - length formula: $s=15\times\frac{7\pi}{30}=\frac{7\pi}{2}\approx\frac{7\times3.14159}{2}=10.995565\approx10.99$ ft.

Answer:

10.99 feet