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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7592
GMAT 1: 760 Q51 V42 GPA: 3.82
There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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1
4 00:00

Difficulty:   35% (medium)

Question Stats: 61% (01:01) correct 39% (00:57) wrong based on 139 sessions

### HideShow timer Statistics Attachment: 1.png [ 2.62 KiB | Viewed 1991 times ]

There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. $$1-π$$
B. $$2-π$$
C. $$4-π$$
D. $$1-(\frac{π}{2})$$
E. $$1-(\frac{π}{4})$$

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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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MathRevolution wrote:
Attachment:
1.png

There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. $$1-π$$
B. $$2-π$$
C. $$4-π$$
D. $$1-(\frac{π}{2})$$
E. $$1-(\frac{π}{4})$$

area of one of the 4 regions shaded = (area of Square - area of circle)/4
= (4-pi)/4 = 1- pi/4

Hence Option E is correct
Hit Kudos if you liked it Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7592
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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==> The area of the square-area of the $$circle=2^2- π=4- π$$, and since it asks for one of the 4 regions shaded, you get $$\frac{4- π}{4}=1-(\frac{π}{4})$$.

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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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Silly mistake- but fixed it- you have to multiply 1 by 1 to get the area of one fourth of the square and then subtract it by the area of the remaining portion of the circle inside it; though, you can just find the area of the circle and divide it by 4. Thus,

1 x 1= 1
pi (1)^2= pi (1) / 4

1- pi(1)/4
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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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Side of square = diameter of circle = 2 x radius\therefore radius = diameter/2 = 1

Area of shaded region = area of square - area of circle = 2 x2 - pi*1*1 = 4 -pi

Since there are 4 equal parts of the shaded region, area of one shaded region = (4 -pi)/4 = 1 - pi/4

Option E

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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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Can someone please explain to me why the area of the circle isnt pi*radius^2? Why is it just pi?
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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teamryan15 wrote:
Can someone please explain to me why the area of the circle isnt pi*radius^2? Why is it just pi?

The area is $$pi*r^2$$ itself but the length of square is 2, which is equal to diameter. Hence radius is 2/2=1
So r^2=1^2=1..
What is left is pi*r^2=pi*1^2=pi
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Re: There is a circle inscribed in a square, shown on the above figure. If  [#permalink]

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MathRevolution wrote:
Attachment:
1.png

There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. $$1-π$$
B. $$2-π$$
C. $$4-π$$
D. $$1-(\frac{π}{2})$$
E. $$1-(\frac{π}{4})$$

Square Area= 4

Area of circle= PI.

1/4 th of shaded region= (1/4) (4_PI) E
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I never gave up what I wanted- Re: There is a circle inscribed in a square, shown on the above figure. If   [#permalink] 01 Jun 2019, 23:19
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