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20 Jul 2018, 00:01
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:04) correct
25%
(01:37)
wrong
based on 56
sessions
History
Date
Time
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Not Attempted Yet
In the figure, ABCD is a rectangle, and BE and CF are arcs of circles centred at A and D. What is the area of the shaded region?
A. \(10 - \pi\)
B. \(2(5 - \pi)\)
C. \(2(5 -2\pi)\)
D. \(6 + 2\pi\)
E. \(5(2 - \pi)\)
Attachment:
2018-07-20_1100.png [ 12.48 KiB | Viewed 5845 times ]
20 Jul 2018, 01:21
Kudos
Bookmarks
Bunuel
we are asked to find out the area of the shaded portion. This can be done as follows :
Area of the shaded portion : Area of the rectangular - Area of the sector of the 2 circles.
Area of the rectangular : 5*2 = 10
Area of the sector of the circle: pie*\((r)^2\) * C/360. Where c is the central angle. As sector is the part of rectangular , central angle must be 90 degree.
= pie * (2)^2 * 90/360.............width of the rectangular has become the radius of the circle.
= pie
but this one is the area of a circle. we have 2 sectors.
So, total area of 2 sectors: 2 pie
Area of the shaded portion : 10 - 2 pie
= 2( 5 - pie )
The best answer is B.
20 Jul 2018, 01:34
Kudos
Bookmarks
Bunuel
Area of rectangle = L*B = 5*2 = 10
Now, the non-shaded region together can be considered a semi-circle or radius 2, since each of the the regions are quarters of the circle with radius 2
Therefore,
Area of both non-shaded region combined = 1/2*pi*r^2 = 1/2*pi*4 = 2*pi
And, Area of shaded region = Area of Rectangle - Area of two quarter circle combined = 10 - 2*pi = 2(5 - pi)
Hence, B.
