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In the figure above, if the area of the smaller circular reg

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In the figure above, if the area of the smaller circular reg [#permalink] New post 06 Oct 2020, 11:30
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In the figure above, if the area of the smaller circular region is \(\frac{1}{2}\) the area of the larger circular region, then the diameter of the larger circle is how many inches longer than the diameter of the smaller circle?

A. \(\sqrt{2}-1\)

B. \(\frac{1}{2}\)

C. \(\frac{\sqrt{2}}{2}\)

D. \(\frac{2-\sqrt{2}}{2}\)

E. \(\sqrt{2}\)
[Reveal] Spoiler: OA

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Re: In the figure above, if the area of the smaller circular reg [#permalink] New post 06 Oct 2020, 20:12
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area of small circle =(1/2)* area of large circle

area of large circle =\(π*(1/2)^2\)=π/4

area of small circle=π/8

diameter of small circle =1/(√2)

diameter of large circle is 1-1/(√2) times greater than small circle

option D is correct
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Re: In the figure above, if the area of the smaller circular reg [#permalink] New post 12 Oct 2020, 11:01
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Assume the big area is 4 and small area will be 2

πr^2=4
r =2

Small circle
πr^2 =2
r =√2

Diameter is 2*r
Hence
Big diameter minus small diameter is
4-2√2

Divide thru by 4(my assumption for the area b4 )
1-2√2/2

LCM will get (2-√2)/2

Ans D

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Re: In the figure above, if the area of the smaller circular reg   [#permalink] 12 Oct 2020, 11:01
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