Question

question 3 (multiple choice worth 1 points) (07.03 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? 5.89 feet 6.23 feet 7.46 feet 8.16 feet

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. First, find the radius from the diameter. Given \( d = 15 \) ft, so \( r=\frac{d}{2}=\frac{15}{2}=7.5 \) ft. The central angle \( \theta = 45^\circ \).

Step2: Substitute values into formula

Substitute \( \theta = 45^\circ \), \( r = 7.5 \) ft into the arc length formula:
\( L=\frac{45^\circ}{360^\circ}\times2\pi\times7.5 \)
Simplify \( \frac{45}{360}=\frac{1}{8} \), so:
\( L=\frac{1}{8}\times2\pi\times7.5=\frac{15\pi}{8} \)
Calculate the numerical value: \( \frac{15\pi}{8}\approx\frac{15\times3.1416}{8}\approx\frac{47.124}{8}\approx5.89 \) ft.

Answer:

5.89 feet