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# Circle O is inscribed in square ABCD as shown above. The area of the s

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Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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10 Jan 2016, 08:10
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:24) correct 33% (01:10) wrong based on 113 sessions

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Circle O is inscribed in square ABCD as shown above. The area of the shaded region is approximately

A. 10
B. 25
C. 30
D. 50
E. 75

Attachment:

2016-01-10_1908.png [ 4.9 KiB | Viewed 1600 times ]

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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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10 Jan 2016, 08:29
Bunuel wrote:

Circle O is inscribed in square ABCD as shown above. The area of the shaded region is approximately

A. 10
B. 25
C. 30
D. 50
E. 75

Attachment:
2016-01-10_1908.png

Area of Inscribed Circle = \pi/4 * Area of square
Area of Square = 10*10= 100
Area of circle = \pi/4*100 = 25\pi

Area of parts outside circle but in square = 100-25\pi =100-75 (Approximately)=25

Area of shaded reason = 25/4=6 (Approximately)

The nearest value to 6 is 10. So in test conditions i will opt for A.

Please let me know where am i making mistakes, if i am doing so. I am not sure if the approximate answers can be so further.
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Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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06 Mar 2017, 20:13
Bunuel wrote:

Circle O is inscribed in square ABCD as shown above. The area of the shaded region is approximately

A. 10
B. 25
C. 30
D. 50
E. 75

Attachment:
2016-01-10_1908.png

Area of square = 100
Area of circle = 25π

Area of the shaded region = $$\frac{(100-25π)}{4}$$ ~ $$\frac{(100-78.75)}{4}$$ ~ $$\frac{21}{4}$$=5.x

Closest is A, which is almost double the calculated value. :S
Can someone help ?
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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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08 Mar 2017, 14:23
2
This question can be solved logically, in my opinion. Instead of using heavy calculation, we can deduce that the radius is 5- that the radius shown doesn't touch the edge of the square is, again in my opinion, an optical illusion. Actually, if you draw a line from the middle point of any side of the square to the center the radius must be 5. Knowing that the radius must be 5, we can segment a portion of the square- 5 by 5 would be the area of the square that the shaded triangle is contained within; hence, through the process of elimination we can arrive at answer "A." Though this is probably a shoddy method when considering a 700 level question.
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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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10 Mar 2017, 12:30
Hi Nunuboy1994,

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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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08 Jul 2017, 05:35
answer should be around 5.25. n none of the option matches.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

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Re: Circle O is inscribed in square ABCD as shown above. The area of the s   [#permalink] 08 Jul 2017, 05:35
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# Circle O is inscribed in square ABCD as shown above. The area of the s

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