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29 May 2018, 06:25
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (01:26) correct
19%
(01:24)
wrong
based on 74
sessions
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If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 – π/4
B) 2 – π/4
C) 2 – π/2
D) 4 – π
E) 4 – 2π
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29 May 2018, 06:38
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Attachment:
bzRq3H2.png [ 12.41 KiB | Viewed 6941 times ]
Formula used:
Area of sector - \(\frac{A}{360} * \pi * r^2\) where A is the angle and r is the radius of the circle
The four circles with centers A,B,C, and D each having a radius of 1,
The 4 radii form a square ABCD with side 2(Area of the square is \(2^2 = 4\))
The area of a sector(with an angle of 90 degree and a radius 1) is \(\frac{90}{360} * \pi * 1^2 = \frac{\pi}{4}\)
Hence, the are of the 4 sectors is \(4 * \frac{\pi}{4}\) = π
The area of the shaded portion is the difference between the area of the square and
the area of 4 sectors. Therefore, the area of the shaded portion is 4 – π(Option D)
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29 May 2018, 11:14
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Attachment:
bzRq3H2.png [ 10.91 KiB | Viewed 6774 times ]
Radius of Circle is 1.
Area of one Circle is \(πr^2\) = \(π*1^2\) = \(π\).
As you can see in the figure - Area of AO1CB = 1/4 * Area of circle = \(\frac{π}{4}\)
Other wise we can also use like this.
Area of region ABCO1 = \(π * r^2 *\frac{θ}{360}\) ( Area of Sector formula)
=\(π * 1^2 *\frac{90}{360}\)
\(\frac{1}{4}\) * Area of Circle =\(\frac{π}{4}\).
Side of Square as mentioned in the figure - 1+1 = 2.
Area of Square is = 2 *2 = 4.
Are of the Circular Region surrounded by square = 4 * Area of region ABCO1
= 4 * \(\frac{π}{4}\)
= \(π\)
Area of Shaded Region = area of square - are of Circular Region surrounded by square
= 4 - \(π\)
Hence D is the ans
