Try this on for size. It's another of the Fairfax County Math League problems:
READ THIS BEFORE COMMENTING!
All comments are subject to approval before they are published, so they will not appear immediately. Comments should be civil, relevant, and substantive. Anonymous comments are not allowed and will be unceremoniously deleted. For more on my comments policy, please see this entry on my other blog.
AND A NEW RULE (per this post): comments critical of Trump's lying must include criticism of Biden's or Kamala's or some prominent leftie's lying on a one-for-one basis! Failure to be balanced means your comment will not be published.
I strained my brain for a few minutes 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.
ReplyDeleteHow 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 = 12.25π
Area of B = (2^2)π = 4π
Area of A = (1.5^2)π = 2.25π
Blue region's area:
[(1/2)(12.25π)] - [(1/2)(4π)] + [(1/2)(2.25π)]
= 5.25π
Red region's area
[(1/2)(12.25π)] + [(1/2)(4π)] - [(1/2)(2.25π)]
= 7π
The ratio of blue to red is thus
5.25/7, 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.
Looks like the Korean flag went on a bender.
ReplyDeleteYep, that's all I've got.
That's pretty much what I thought when I saw the black-and-white original.
ReplyDeleteWill be posting the original soon; I brought the sheet home with me from school.
By the way, 3/4 is confirmed as correct. The original comment I wrote for this problem came to the correct solution, but I had forgotten to calculate area by using radii, not diameters. All my calculations were off by a factor of 2, which turned out not to matter since you lose the 2 once you establish the ratio.
ReplyDelete