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Updated on: 05 Mar 2015, 10:06
Originally posted by pacifist85 on 05 Mar 2015, 10:00.
Last edited by Bunuel on 05 Mar 2015, 10:06, edited 1 time in total.
Last edited by Bunuel on 05 Mar 2015, 10:06, edited 1 time in total.
Edited the question.
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B
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77% (01:39) correct
23%
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A circle of radius r is inscribed in a square, as shown below. 
Geometry_Q1_Image.jpg [ 4.2 KiB | Viewed 20947 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) %
Attachment:
Geometry_Q1_Image.jpg [ 4.2 KiB | Viewed 20947 times ]
A. [(50 *π) / r] %
B. (25 * π) %
C. (50*π) %
D. (25 / r) %
E. (25 * r) %
Updated on: 05 Mar 2015, 10:10
Originally posted by pacifist85 on 05 Mar 2015, 10:10.
Last edited by pacifist85 on 05 Mar 2015, 10:10, edited 1 time in total.
Last edited by pacifist85 on 05 Mar 2015, 10:10, edited 1 time in total.
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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
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
05 Mar 2015, 10:10
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pacifist85
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.
Answer: B.
