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Circle A is in the interior of circle B. The diameter of circle B is 16 cm. What is the diameter of circle A for which the ratio of the shaded area to the area of circle A is 3:1?

 

 Jan 13, 2019

Best Answer 

 #1
avatar+4299 
+2

We know that the area of the shaded region plus the area of circle A equals the Area of Circle B. Since the shaded area: area of the circle, 3:1, we have \(3x+x=64\pi\)\(4x=64\pi, x=16\pi\) . Directly, we \(\)get  \(\pi*r^2=16\pi\), so \(r^2=16, r=4.\) Remember that length can't be negative! Thus, the diameter of circle A is \(4*2=\boxed{8}\) cm.

 Jan 13, 2019
 #1
avatar+4299 
+2
Best Answer

We know that the area of the shaded region plus the area of circle A equals the Area of Circle B. Since the shaded area: area of the circle, 3:1, we have \(3x+x=64\pi\)\(4x=64\pi, x=16\pi\) . Directly, we \(\)get  \(\pi*r^2=16\pi\), so \(r^2=16, r=4.\) Remember that length can't be negative! Thus, the diameter of circle A is \(4*2=\boxed{8}\) cm.

tertre Jan 13, 2019
 #2
avatar+102320 
+1

Nice, tertre....!!!

 

cool cool cool

 Jan 13, 2019
 #3
avatar+4299 
+1

Thank you, CPhill!

tertre  Jan 13, 2019

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