October 28, 2002
Problem of the Month

The Merry-Go-Round Problem

A man wants to paint the floor of a Merry-Go-Round.   It is formed by two concentric circles (an annulus).   He wants to determine the area of the floor (shown in yellow in the figure below), so he will know how much paint to buy.

Because of all the machinery in the middle, he is unable to measure the radii of the two circles.   However, he finds the length of a special chord to be 70 feet.   This special chord is a chord of the larger circle and a tangent to the smaller circle.   (See diagram below).

Can you determine the area of the Merry-Go-Round which needs to be painted from just that one measurement?

Solution to the Problem:

The area to be painted is 3,848.45 square feet.

Correctly solved by:

1. Keith Mealy	Cincinnati, Ohio
2. Rick Jones	Kennett Square, Pennsylvania
3. Adam Carter	Fort Wayne, Indiana
4. Christopher March	Virginia Tech, Blacksburg, Virginia
5. Richard K. Johnson	La Jolla, California
6. Jeff Gaither	Winchester, Virginia
7. Tina Zahel	Winchester, Virginia
8. Subhash M. Parmar	Basildon, Essex, England, United Kingdom
9. James Alarie	University of Michigan -- Flint Flint, Michigan
10. David & Judy Dixon	Bennettsville, South Carolina
11. Eva Cheng	Benenden, Cranbrook, Kent, United Kingdom
12. Geoff Keith	Santa Monica, California
13. John Funk	Ventura, California
14. Gary Pounder	Seattle, Washington
15. Kyle Martin	North Andover, Massachussetts
16. Ashley Neumann	Winchester, Virginia
17. Tom Hanzl	Czech republic
18. Katie Nickerson	North Adams, Massachussetts

Send any comments or questions to: David Pleacher