Answer to October 28, 2002 Problem

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