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13 Sep 2018, 04:47
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:34) correct
31%
(02:00)
wrong
based on 83
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If the four circles shown above touch two other circles at exactly one point each and have a radius of 5, and the centers of each pair of opposite circles are the same distance apart, what is the approximate area of the shaded region?
A. 76
B. 50
C. 36
D. 25
E. 22
Attachment:
image036.jpg [ 4.66 KiB | Viewed 3429 times ]
Updated on: 15 Sep 2018, 09:02
Originally posted by AvidDreamer09 on 15 Sep 2018, 01:23.
Last edited by AvidDreamer09 on 15 Sep 2018, 09:02, edited 3 times in total.
Last edited by AvidDreamer09 on 15 Sep 2018, 09:02, edited 3 times in total.
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Area of the shaded region = area of the square with vertex at the center - area of 4 quarters of the circle (or one circle)
Area of the circle\(=πr^2=25π\)
Side of the square with Vertex at the center of the circle side of the square = 2r = d
Area of the square with Vertex \(= d^2*d^2 = 100\)
\(100-(25*22)/7=(700-550)/7 = 150/7 = 21.4 = approx 22\)
Area of the circle\(=πr^2=25π\)
Side of the square with Vertex at the center of the circle side of the square = 2r = d
Area of the square with Vertex \(= d^2*d^2 = 100\)
\(100-(25*22)/7=(700-550)/7 = 150/7 = 21.4 = approx 22\)
15 Sep 2018, 06:58
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Attachment:
SquareCircle.jpg [ 10.75 KiB | Viewed 3159 times ]
Area(Shaded region) = Area(Square with side 10) - Area(4 quarter circles or 1 circle with radius 5)
Formula used:
Area of a square = \(side^2\)
Area of a quarter circle = \(\frac{1}{4} * \pi * r^2\) where r - radius
Substituting values, Area(Square) = \(10^2 = 100\)
Area of each quarter circle = \(\frac{1}{4} * \pi * 5^2 = \frac{1}{4} * \frac{22}{7} * 25 = \frac{275}{14} = 19.5\)(apprx)
Since we have four quarter circles, the total area enclosed by them is \(4*19.5 = 78\)
Therefore, the area of the shaded region which is the difference in areas is 100 - 78 = 22(Option E)
i am back 
how did you get \(\frac{22}{7}\) ? 
what it means ? 
