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Updated on: 24 Jul 2013, 11:17
Originally posted by genuinebot85 on 24 Jul 2013, 11:14.
Last edited by Bunuel on 24 Jul 2013, 11:17, edited 1 time in total.
Last edited by Bunuel on 24 Jul 2013, 11:17, edited 1 time in total.
Edited the question.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Four identical circles are drawn in a square such that each circle touches two sides of the square and two other circles (as shown in the figure below). If the side of the square is of length 20 cm, what is the area of the shaded region?
(A) 400 – 100π
(B) 200 – 50π
(C) 100 – 25π
(D) 8π
(E) 4π
Could not understand the solution, need help.
Attachment:
File comment: This is the figure for the question.
GeometryPost12Ques2.jpg [ 7.89 KiB | Viewed 83889 times ]
GeometryPost12Ques2.jpg [ 7.89 KiB | Viewed 83889 times ]
(A) 400 – 100π
(B) 200 – 50π
(C) 100 – 25π
(D) 8π
(E) 4π
Could not understand the solution, need help.
24 Jul 2013, 11:35
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genuinebot85
Four identical circles are drawn in a square such that each circle touches two sides of the square and two other circles (as shown in the figure below). If the side of the square is of length 20 cm, what is the area of the shaded region?
(A) 400 – 100π
(B) 200 – 50π
(C) 100 – 25π
(D) 8π
(E) 4π
Could not understand the solution, need help.
(A) 400 – 100π
(B) 200 – 50π
(C) 100 – 25π
(D) 8π
(E) 4π
Could not understand the solution, need help.
Look at the image below:
Attachment:
Untitled.png [ 13.57 KiB | Viewed 64500 times ]
The area of the square = \(20^2 = 400\).
The area of four circles = \(4*(\pi{r^2})=4*(\pi{5^2})=100\pi\) (the diameter of each circle is 1/2 of the side, thus the radius of each circle is 1/4 of the side).
The area of 16 regions = \(400-100\pi\).
The area of shaded region (4 regions with red dots) = \(\frac{400-100\pi}{4}=100-25\pi\).
Answer: C.
Else you could simply find the area of the smaller square (1/4 of the bigger) and subtract the area of the circle. This way you'd also get the area of 4 regions with red dots.
Hope it's clear.
General Discussion
05 Aug 2014, 09:59
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genuinebot85
Four identical circles are drawn in a square such that each circle touches two sides of the square and two other circles (as shown in the figure below). If the side of the square is of length 20 cm, what is the area of the shaded region?
(A) 400 – 100π
(B) 200 – 50π
(C) 100 – 25π
(D) 8π
(E) 4π
Could not understand the solution, need help.
Attachment:
GeometryPost12Ques2.jpg
(A) 400 – 100π
(B) 200 – 50π
(C) 100 – 25π
(D) 8π
(E) 4π
Could not understand the solution, need help.
You can draw a second square, with vertices at the centers of the circles. Then that square has sides of 10 units, and the quarter circles have total area of 25*pi.
Ans C 
