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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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35% (medium)

Question Stats:

74% (01:52) correct 26% (02:32) wrong based on 106 sessions

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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]

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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]

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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]

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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
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Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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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
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Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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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
To determine if the text passage contains a mathematical question and if an answer is provided, let's analyze the content step by step.

### Content Structure:
The text is a GMAT question of the day, which includes a problem statement and a set of answer choices. The problem statement is a geometry question about the area of a square inscribed in a circle.

### Analysis:
1. **Mathematical Question**: The passage contains a mathematical question: "The area of the circumscribed circle in the figure above is 32. What is the area of the square?"
2. **Answer Provided**: The passage provides a set of answer choices (A, B, C, D, E) for the question.

### Conclusion:
The text contains a single mathematical question and provides multiple answer choices for that question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Feb 2019, 12:05

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February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

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The area of the circumscribed circle in the figure above is 32. What

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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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 ]

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Status: GMATINSIGHT Tutor
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GMAT: INSIGHT
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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

_________________

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]

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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]

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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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The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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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]

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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
user
To determine if the text passage contains a mathematical question and if an answer is provided, let's analyze the content step by step.

### Content Structure:
The text is a GMAT question of the day, which includes a problem statement and a set of answer choices. The problem statement is a geometry question about the area of a square inscribed in a circle.

### Analysis:
1. **Mathematical Question**: The passage contains a mathematical question: "The area of the circumscribed circle in the figure above is 32. What is the area of the square?"
2. **Answer Provided**: The passage provides a set of answer choices (A, B, C, D, E) for the question.

### Conclusion:
The text contains a single mathematical question and provides multiple answer choices for that question.

TYPE: SINGLE_QUESTION_WITH_ANSWER