Problem:
Margie's winning art design is shown. The smallest circle has radius 2 inches, with each successive circle's radius increasing by 2 inches. Approximately what percent of the design is black?
Answer Choices:
A. 42
B. 44
C. 45
D. 46
E. 48
Solution:
Circle #123456βRadius24681012βArea4Ο16Ο36Ο64Ο100Ο144Οββ
The total black area is 4Ο+(36β16)Ο+(100β64)Ο=60Οin2.
So the percent of the design that is black is 100Γ144Ο60Οβ=100Γ125β or about 42%.
Answer: Aβ.
The problems on this page are the property of the MAA's American Mathematics Competitions
.jpg)