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A circle of radius r is inscribed in a square, as shown below.

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Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 415
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
A circle of radius r is inscribed in a square, as shown below.  [#permalink]

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Updated on: 05 Mar 2015, 09:06
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A circle of radius r is inscribed in a square, as shown below.
Attachment:

Geometry_Q1_Image.jpg [ 4.2 KiB | Viewed 11784 times ]

What percent of the square’s area is taken up by the circle?

A. [(50 *π) / r] %

B. (25 * π) %

C. (50*π) %

D. (25 / r) %

E. (25 * r) %

Originally posted by pacifist85 on 05 Mar 2015, 09:00.
Last edited by Bunuel on 05 Mar 2015, 09:06, edited 1 time in total.
Edited the question.
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 415
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
A circle of radius r is inscribed in a square, as shown below.  [#permalink]

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Updated on: 05 Mar 2015, 09:10
So,

Starting with the area of the circle, which is the easy one, it is πr^2

Since the radius is r, the diameter of the circle is 2r.
The diameter of the circle is also equal to the side of the square.
Since the area of the suare is side^2, then the area of the particular square will be (2r)^2 = 4r^2.

So the area of the circles takes up this % of the area of the square:

πr^2 / 4r^2 = (1/4)π = 25π%, So, ANS B

Originally posted by pacifist85 on 05 Mar 2015, 09:10.
Last edited by pacifist85 on 05 Mar 2015, 09:10, edited 1 time in total.
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Joined: 02 Sep 2009
Posts: 53063
A circle of radius r is inscribed in a square, as shown below.  [#permalink]

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05 Mar 2015, 09:10
pacifist85 wrote:
A circle of radius r is inscribed in a square, as shown below.

What percent of the square’s area is taken up by the circle?

A. [(50 *π) / r] %

B. (25 * π) %

C. (50*π) %

D. (25 / r) %

E. (25 * r) %

Radius of r, means that the side is 2r.

The area of square (2r)^2 = 4r^2;
The area of circle πr^2.

The percent of the square’s area is taken up by the circle = circle/square*100 = πr^2/4r^2*100= π/4 * 100 = 25π.

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Re: A circle of radius r is inscribed in a square, as shown below.  [#permalink]

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23 Dec 2017, 17:47
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Re: A circle of radius r is inscribed in a square, as shown below.   [#permalink] 23 Dec 2017, 17:47
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A circle of radius r is inscribed in a square, as shown below.

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