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Sep 06, 2014
10:15 AM | | | ; |
I strained my brain for a few mietnus after class trying to figure this one out... and then my colleague strolled over and told me how easy it was. Think of it this way: all the circles` centers lie on the same line, so you need to think in terms of semicircles.How do I find the area of the blue region, for example? I need to calculate the area of Circle C, which is the biggest circle. Then I need to calculate the respective areas of Circles A and B. Next, I need to subtract half the area of Circle B from half the area of Circle C, and I also need to add half the area of Circle A.Then we figure it the other way for red.Hell, let`s do this.Based on the ratios given, we know the diameter of Circle C is 7. So...Area of C = (3.5^2)π = 12.25πArea of B = (2^2)π = 4πArea of A = (1.5^2)π = 2.25πBlue region`s area:[(1/2)(12.25π)] - [(1/2)(4π)] + [(1/2)(2.25π)]= 5.25πRed region`s area[(1/2)(12.25π)] + [(1/2)(4π)] - [(1/2)(2.25π)]= 7πThe ratio of blue to red is thus5.25/7, or 21/28, or 3/4.That`s a lot of work merely to confirm what I had initially suspected! Without doing any math-- and before my colleague had shown me the light-- I had thought the answer would be either 3/4 or 9/16, based purely on the info we were given about the respective diameters of Circles A and B, and my assumptions about the areas of those circles.So there we are. I`ll need to confirm this answer, but I`m pretty sure I`m right.
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