Problem:
Rectangle has sides and . A circle of radius is centered at , a circle of radius is centered at , and a circle of radius is centered at . Which of the following is closest to the area of the region inside the rectangle but outside all three circles?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The areas of the quarter-circles are and . Their total area is . Using as an approximation of , this is , leaving for the desired area. (Using for yields .)
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions