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# Geometry

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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 8:1?

Oct 24, 2021

#1
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The diameter should be 3.

Oct 24, 2021
#2
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Hello Guest!

$$r_B=8cm\\\ d_A=x\\ (\pi \cdot64cm^2-\pi \cdot \dfrac{x^2}{4} ):(\pi \cdot \dfrac{x^2}{4})=8:1\\ \pi \cdot64cm^2-\pi \cdot \dfrac{x^2}{4} =2\pi x^2\\ \pi \cdot64cm^2=\dfrac{9\pi x^2}{4}\\ 8cm=\dfrac{3x}{2}$$

$$x=5\dfrac{1}{3}cm$$

The diameter of circle A is 5.33cm.

!

Oct 24, 2021