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 #123456​Radius24681012​Area4π16π36π64π100π144π​​
The total black area is 4π+(36−16)π+(100−64)π=60πin2.
So the percent of the design that is black is 100×144π60π​=100×125​ or about 42%.
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions
.jpg)