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Help!

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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

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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
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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
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Nice, tertre....!!!   Jan 13, 2019
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Thank you, CPhill!

tertre  Jan 13, 2019