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Circles of diameter 1 inch and 3 inches have the same center. The smaller circle is painted red, and the portion outside the smaller circle and inside the larger circle is painted blue. What is the ratio of the blue-painted area to the red-painted area?

 

 Jul 24, 2020
edited by MathWizPro  Jul 24, 2020
edited by MathWizPro  Jul 24, 2020
 #1
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To find area, we need the radius of the circle. The radius of the red circle is 1/2 of the diameter 1, which is 1/2. The radius of the blue circle is 1/2 of the diameter 3, which is 3/2. The area of the red circle is (1/2)^2pi=1/4pi. The area of the blue circle is (3/2)^2pi=9/4pi. However, the blue area is 9/4pi-1/4pi=8/4pi=2pi. So the ratio fo the blue area to the red is 2pi:1/4pi=8.

 Jul 24, 2020
 #2
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Thanks! 

laughsmiley

MathWizPro  Jul 24, 2020

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