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In the figure shown, what is the difference between the areas of the s

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In the figure shown, what is the difference between the areas of the s  [#permalink]

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New post 18 Apr 2018, 12:18
1
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

42% (03:08) correct 58% (02:08) wrong based on 21 sessions

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In the figure above, what is the difference between the areas of the shaded regions A and B?

A. \(\frac{(35\pi - 50)}{2}\)
B. \(\frac{(35\pi - 40)}{2}\)
C. \(\frac{(65\pi - 100)}{4}\)
D. \(\frac{(30\pi - 50)}{2}\)
E. \(\frac{(75\pi - 200)}{8}\)

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Re: In the figure shown, what is the difference between the areas of the s  [#permalink]

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New post 18 Apr 2018, 19:08
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Nice question. I'm so used to dealing with straight lines that the curved lines forced my brain to work a little extra.

We need to find: (Area of Region A) - (Area of Region B)
Approach: (Area of small semi-circle) - (Area of one of the corners)
Calculation: \(\frac{(2.5)^2π}{2}-\frac{10*10-5^2π}{4}=\frac{6.25π}{2}-\frac{100-25π}{4}=\frac{12.5π-100+25π}{4}=\frac{37.5π-100}{4}=\frac{75π-200}{8}\)

Answer: E
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Re: In the figure shown, what is the difference between the areas of the s  [#permalink]

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New post 19 Apr 2018, 04:00
Area B=area of square - (1/4area of bigger circle + 1/2 area of smaller circle - areaA)
Ans=e

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Re: In the figure shown, what is the difference between the areas of the s &nbs [#permalink] 19 Apr 2018, 04:00
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In the figure shown, what is the difference between the areas of the s

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