1. How Much Shorter from the Center (Vertical) Line Is Point B Than Point A?

A Carousel Problem

Ann is making plans to build a carousel for a new amusement park. The specifications are that the carousel be built of wood, be at least 40’ in diameter and that it should seat at least 20 people at a time.

Ann plans to make the 40’ solid flooring of large oak planks that are 1’ wide. Clearly, she will need 40 planks, but she hopes to save money by only buying the minimum length she needs for each plank. The middle two planks must be 40’ long, but she will need to shave off a curved part of this plank in order to create the circular base she needs. (See the attached Sketchpad illustration.)

1. How much shorter from the center (vertical) line is point B than point A?

2. So what must the length of the next plank be?

3. What is the measure of the angle AOB in degrees?

4. What is the measure of AOB in radians?

5. What is the length of the arc AB?

6. How much shorter from the center line is point C than point B?

7. So what must the length of the next plank be?

8. What is the measure of AOC in degrees?

9. What is the measure of AOC in radians?

10. So what is the measure of BOC in degrees/radians?

11. And what is the length of arc BC?

12. Explain how to use your calculator efficiently to complete the table on the back. Board Longest Longest length Shortest length Central angle Board’s arc Number edge from center line from center line measure length 1 40 20 19.975’ 2.86598 1.00042 2 3 4 5 6 2.98009 7 8 9 18.3303 10 1.13667 11 12 16 13 14 15 16 12 17 24 18 19 20

13. Find and explain the sum of the angle measures.

14. Find and explain the sum of the arc lengths.

15. Ann has 24 horses that she would like to place on her carousel. If she places them 2’ from the edge of the carousel, what is the distance between the horses?

How many horses do you think Ann should place on her carousel? Explain your answer.

16. If she wants the carousel to make 2 revolutions per minute, how fast will those horses be traveling in miles per hour?

17. If she wants the horses to travel 5 miles per hour, how fast must the carousel turn? E D C B A O