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Question

Margie's winning art design is shown. The smallest circle has radius 2 inches, with each successive circle's radius increasing by 2 inches. Which of the following is closest to the percent of the design that is black? FIGURE

Accepted Answer

Let the smallest circle be 1, the second smallest circle be 2, the third smallest circle be 3, etc. arrayc|cc circle # & radius & area 1 & 2 & 4 2 & 4 & 16 3 & 6 & 36 4 & 8 & 64 5 & 10 & 100 6 & 12 & 144 array The entire circle's area is 144. The area of the black regions is (100-64) + (36-16) + 4 = 60. The percentage of the design that is black is 60144 = 512 42.