Question

13 multiple choice 1 point a hula hoop has a radius of 19 inches. what is the length of the arc subtending 1/4 of the hoop? 29.8 inches 14.9 inches 43.8 inches 59.7 inches

Explanation:

Step1: Recall the formula for arc length

The formula for arc length \(L\) is \(L = r\theta\) (where \(r\) is the radius and \(\theta\) is the central angle in radians). Since the arc subtends \(\frac{1}{4}\) of the hoop, \(\theta=\frac{1}{4}\times2\pi=\frac{\pi}{2}\) radians and \(r = 19\) inches.

Step2: Calculate the arc length

Substitute \(r = 19\) and \(\theta=\frac{\pi}{2}\) into the formula \(L=r\theta\). So \(L=19\times\frac{\pi}{2}\). Using \(\pi\approx3.14\), we have \(L = 19\times\frac{3.14}{2}=19\times1.57 = 29.83\approx29.8\) inches.

Answer:

29.8 inches