Problem:
Rolly wishes to secure his dog with an -foot rope to a square shed that is feet on each side. His preliminary drawings are shown.
Which of these arrangements gives the dog the greater area to roam, and by how many square feet?
Answer Choices:
A. I, by
B. I, by
C. II, by
D. II, by
E. II, by
Solution:
The regions in which the dog can roam for each arrangement are shaded in the figure. For arrangement I, the area of this region is square feet. The area of the shaded region in arrangement II exceeds this by the area of a quarter-circle of radius feet, that is, by square feet.
The problems on this page are the property of the MAA's American Mathematics Competitions