POD Presentation Week 18 Problem 1

Problem At the Circus, a performer twirls a Hula-Hoop around her arm. Assume the Hula-Hoop has a radius of 18 inches and the performer’s arm is completely round with a diameter of 4.5 inches. If point A of the hula Hoop is currently touching the performer’s arm, after how many revolutions around her arm will point A first be on the performer’s arm again?

Step 1 First, I know that the formula for finding the circumference of a circle is c=pi *diameter. The diameter of the hula-Hoop is 36 because the radius is 18, and radius times 2 gives you the diameter. To find the circumference, I multiplied pi times 36. to make my answer exact, I left my answer in terms of pi: 36pi. I did this because I knew that if I divided the circumferences of the 2 circles, the quotient would be my answer.

Step 2 Next, I wanted to find the circumference of the smaller circle, the performer’s arm. The diameter is already labeled in the drawing: 4.5 inches. Next, I used the formula for finding circumference: 4.5 * pi. Once again, I wanted my answer to be exact, not rounded, so I left it in terms of pi: 4.5pi.

Step 3 Now, I know that if I divide the circumferences of the 2 circles, I would get my answer. Since I now have the circumferences of both circles, all I have to do is divide. 36/4.5=8. So, it will take the performer 8 revolutions of the hula-hoop before Point A is back on her arm.