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  The area of the circumscribed circle in the figure above is 32. What
  
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  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
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  06 Sep 2018, 00:15
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  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  
  image001 (1).jpg [ 2.78 KiB | Viewed 1057 times ]
  
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  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
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  06 Sep 2018, 02:07
  1
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Area of the circle = πr^2 = 32
  
  i.e. r = √(32/π)
  
  Diagonal of the Square = a√2 (where a is the side of square) = Diameter of circle = 2*r
  
  i.e. a√2 = 2*√(32/π)
  
  i.e. a = 8/√π
  
  Area of the square = a^2 = (8/√π)^2 = 64/π
  
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  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
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  06 Sep 2018, 03:02
  +1 for D.
  
  Area of Circle = π* r^2 = 32, r = √(32/π), and d = 2*√(32/π)
  Now, Area of Square = d^2 / 2 = ((4*32) / π) / 2 = 64 / π
  
  Hence, D.
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  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  06 Sep 2018, 06:38
  1
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  The attachment image001 (1).jpg is no longer available
  Attachment:
  
  image001 %281%29.jpg [ 5.83 KiB | Viewed 860 times ]
  So Radius is $$\frac{a√2}{2}$$
  
  Now, Area of the Circle is $$\frac{2a^2π}{4}=32$$
  
  Or, $$a^2π=64$$
  
  Or, $$a^2=\frac{64}{π}$$ = Area of the square , Answer must be (D)
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  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  20 Oct 2018, 23:17
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Area of Circle is 32
  
  A. $$\frac{8}{\pi}$$ : approx 3 unit
  
  B. $$\frac{8\sqrt{2}}{\pi}$$ : approx 4 units
  
  C. $$\frac{32}{\pi}$$ : around 10 or 11
  
  D. $$\frac{64}{\pi}$$ : approx 22
  
  E. 32 : not possible
  
  Only seems to be a correct choice..
  
  sometimes we can save a lot of time just by using simple ways.. ONLY SOMETIMES..
  VP
  Joined: 09 Mar 2016
  Posts: 1286
  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  21 Oct 2018, 01:46
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Formula used to calculate the area of circumscribed square $$2*r^2$$ where r is radius of circle
  
  Dagonal of square is equal to diameter of circle
  
  Area of Circle $$\pi*r^2$$ =$$32$$
  
  Taking square root on both sides
  $$\sqrt{\pi*r^2}$$ = $$\sqrt{32}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$\sqrt{16*2}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$4\sqrt{2}$$
  
  so r = $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$
  
  2 * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ = $$\frac{2 *32}{\pi}$$ = $$\frac{64}{\pi}$$
  
  Bunuel pushpitkc can you pls format my explanation - (the square roots/ radicals/ fractions in a math friendly way
  
  thank you
  Senior PS Moderator
  Joined: 26 Feb 2016
  Posts: 3341
  Location: India
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  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  21 Oct 2018, 03:41
  1
  dave13 wrote:
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Formula used to calculate the area of circumscribed square $$2*r^2$$ where r is radius of circle
  
  Dagonal of square is equal to diameter of circle
  
  Area of Circle $$\pi*r^2$$ =$$32$$
  
  Taking square root on both sides
  $$\sqrt{\pi*r^2}$$ = $$\sqrt{32}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$\sqrt{16*2}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$4\sqrt{2}$$
  
  so r = $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$
  
  2 * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ = $$\frac{2 *32}{\pi}$$ = $$\frac{64}{\pi}$$
  
  Bunuel pushpitkc can you pls format my explanation - (the square roots/ radicals/ fractions in a math friendly way
  
  thank you
  
  dave13 - Indeed, a nice way to solve the problem. Edited your solution
  _________________
  
  You've got what it takes, but it will take everything you've got
  
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  Joined: 06 Oct 2017
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  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  15 Nov 2018, 16:06
  GMATinsight wrote:
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Area of the circle = πr^2 = 32
  
  i.e. r = √(32/π)
  
  Diagonal of the Square = a√2 (where a is the side of square) = Diameter of circle = 2*r
  
  i.e. a√2 = 2*√(32/π)
  
  i.e. a = 8/√π
  
  Area of the square = a^2 = (8/√π)^2 = 64/π
  
  Im having immense difficulty with this question. I follow up to this point
  
  i.e. a√2 = 2*√(32/π)
  
  i.e. a = 8/√π
  
  How did you arrive at 8/√π ?
  
  Your help would be greatly appreciated!
  Re: The area of the circumscribed circle in the figure above is 32. What   [#permalink] 15 Nov 2018, 16:06
  Display posts from previous: Sort by
explanation: The provided text is a GMAT question and its solution. The question asks for the area of a square inscribed in a circle, given the area of the circle. The solution involves calculating the radius of the circle, using it to find the side length of the square, and then determining the area of the square.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: GMAT Question of the Day - Daily to your Mailbox; hard ones only
  
   It is currently 17 Feb 2019, 12:05
  
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  The area of the circumscribed circle in the figure above is 32. What
  
  Author Message
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  Math Expert
  Joined: 02 Sep 2009
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  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  06 Sep 2018, 00:15
  00:00
  
  Difficulty:
  
  35% (medium)
  
  Question Stats:
  
  74% (01:52) correct 26% (02:32) wrong based on 106 sessions
  
  HideShow timer Statistics
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  
  image001 (1).jpg [ 2.78 KiB | Viewed 1057 times ]
  
  _________________
  CEO
  Status: GMATINSIGHT Tutor
  Joined: 08 Jul 2010
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  Location: India
  GMAT: INSIGHT
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  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  06 Sep 2018, 02:07
  1
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Area of the circle = πr^2 = 32
  
  i.e. r = √(32/π)
  
  Diagonal of the Square = a√2 (where a is the side of square) = Diameter of circle = 2*r
  
  i.e. a√2 = 2*√(32/π)
  
  i.e. a = 8/√π
  
  Area of the square = a^2 = (8/√π)^2 = 64/π
  
  _________________
  
  Prosper!!!
  GMATinsight
  Bhoopendra Singh and Dr.Sushma Jha
  e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
  Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
  http://www.GMATinsight.com/testimonials.html
  
  ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
  
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  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  06 Sep 2018, 03:02
  +1 for D.
  
  Area of Circle = π* r^2 = 32, r = √(32/π), and d = 2*√(32/π)
  Now, Area of Square = d^2 / 2 = ((4*32) / π) / 2 = 64 / π
  
  Hence, D.
  _________________
  
  The few, the fearless !
  
  Thanks
  
  Board of Directors
  Status: QA & VA Forum Moderator
  Joined: 11 Jun 2011
  Posts: 4383
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  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  06 Sep 2018, 06:38
  1
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  The attachment image001 (1).jpg is no longer available
  Attachment:
  
  image001 %281%29.jpg [ 5.83 KiB | Viewed 860 times ]
  So Radius is $$\frac{a√2}{2}$$
  
  Now, Area of the Circle is $$\frac{2a^2π}{4}=32$$
  
  Or, $$a^2π=64$$
  
  Or, $$a^2=\frac{64}{π}$$ = Area of the square , Answer must be (D)
  _________________
  
  Thanks and Regards
  
  Abhishek....
  
  PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
  
  How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
  
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  Joined: 01 Feb 2018
  Posts: 75
  Location: India
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  GPA: 4
  WE: Consulting (Consulting)
  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  20 Oct 2018, 23:17
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Area of Circle is 32
  
  A. $$\frac{8}{\pi}$$ : approx 3 unit
  
  B. $$\frac{8\sqrt{2}}{\pi}$$ : approx 4 units
  
  C. $$\frac{32}{\pi}$$ : around 10 or 11
  
  D. $$\frac{64}{\pi}$$ : approx 22
  
  E. 32 : not possible
  
  Only seems to be a correct choice..
  
  sometimes we can save a lot of time just by using simple ways.. ONLY SOMETIMES..
  VP
  Joined: 09 Mar 2016
  Posts: 1286
  The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  21 Oct 2018, 01:46
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Formula used to calculate the area of circumscribed square $$2*r^2$$ where r is radius of circle
  
  Dagonal of square is equal to diameter of circle
  
  Area of Circle $$\pi*r^2$$ =$$32$$
  
  Taking square root on both sides
  $$\sqrt{\pi*r^2}$$ = $$\sqrt{32}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$\sqrt{16*2}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$4\sqrt{2}$$
  
  so r = $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$
  
  2 * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ = $$\frac{2 *32}{\pi}$$ = $$\frac{64}{\pi}$$
  
  Bunuel pushpitkc can you pls format my explanation - (the square roots/ radicals/ fractions in a math friendly way
  
  thank you
  Senior PS Moderator
  Joined: 26 Feb 2016
  Posts: 3341
  Location: India
  GPA: 3.12
  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  21 Oct 2018, 03:41
  1
  dave13 wrote:
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Formula used to calculate the area of circumscribed square $$2*r^2$$ where r is radius of circle
  
  Dagonal of square is equal to diameter of circle
  
  Area of Circle $$\pi*r^2$$ =$$32$$
  
  Taking square root on both sides
  $$\sqrt{\pi*r^2}$$ = $$\sqrt{32}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$\sqrt{16*2}$$
  
  i.e $${\sqrt{\pi}}*r$$= $$4\sqrt{2}$$
  
  so r = $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$
  
  2 * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ = $$\frac{2 *32}{\pi}$$ = $$\frac{64}{\pi}$$
  
  Bunuel pushpitkc can you pls format my explanation - (the square roots/ radicals/ fractions in a math friendly way
  
  thank you
  
  dave13 - Indeed, a nice way to solve the problem. Edited your solution
  _________________
  
  You've got what it takes, but it will take everything you've got
  
  Intern
  Joined: 06 Oct 2017
  Posts: 44
  GPA: 3.6
  Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]
  
  Show Tags
  
  15 Nov 2018, 16:06
  GMATinsight wrote:
  Bunuel wrote:
  
  The area of the circumscribed circle in the figure above is 32. What is the area of the square?
  
  A. $$\frac{8}{\pi}$$
  
  B. $$\frac{8\sqrt{2}}{\pi}$$
  
  C. $$\frac{32}{\pi}$$
  
  D. $$\frac{64}{\pi}$$
  
  E. 32
  
  Attachment:
  image001 (1).jpg
  
  Area of the circle = πr^2 = 32
  
  i.e. r = √(32/π)
  
  Diagonal of the Square = a√2 (where a is the side of square) = Diameter of circle = 2*r
  
  i.e. a√2 = 2*√(32/π)
  
  i.e. a = 8/√π
  
  Area of the square = a^2 = (8/√π)^2 = 64/π
  
  Im having immense difficulty with this question. I follow up to this point
  
  i.e. a√2 = 2*√(32/π)
  
  i.e. a = 8/√π
  
  How did you arrive at 8/√π ?
  
  Your help would be greatly appreciated!
  Re: The area of the circumscribed circle in the figure above is 32. What   [#permalink] 15 Nov 2018, 16:06
  Display posts from previous: Sort by
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a GMAT question and its solution. The question asks for the area of a square inscribed in a circle, given the area of the circle. The solution involves calculating the radius of the circle, using it to find the side length of the square, and then determining the area of the square.
  
  Label: question-and-answer