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If each curved side in the figure above is a semicircle with
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20 Jun 2018, 09:35
20 Jun 2018, 09:35
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73% (01:09) correct
26% (01:20) wrong based on 96 sessions
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If each curved side in the figure above is a semicircle with radius 20, and the two parallel sides each have length 100, what is the area of the shaded region?
(A) \(2,000\)
(B) \(4,000\)
(C) \(2,000 - 200\pi\)
(D) \(4,000 - 200\pi\)
(E) \(4,000 - 400\pi\)
Re: If each curved side in the figure above is a semicircle with
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23 Jun 2018, 07:37
23 Jun 2018, 07:37
2
Carcass wrote:
Attachment:
The attachment semi.jpg is no longer available
If each curved side in the figure above is a semicircle with radius 20, and the two parallel sides each have length 100, what is the area of the shaded region?
(A) \(2,000\)
(B) \(4,000\)
(C) \(2,000 - 200\pi\)
(D) \(4,000 - 200\pi\)
(E) \(4,000 - 400\pi\)
Here,
Let us calculate the whole figure as one with 2 semicircle(1 shaded in red and other in black) and 1 rectangle (Please refer to the picture attached) and then after calculating the area's of each one of them we can deduct the semicircle (shaded in red)which will left us with the area of the shaded region
First let us calculate the area of the semicircle = \(\pi r^2\)/2
here radius = 20
therefore the area of the semicircle down =\(200\pi\) and the semicircle of the top (red shaded) =\(200\pi\)
and the area of the circle
Now the area of the rectangle (including the semicircle red shaded)= L *B
we know Length = 100
And Breadth = 40 since the radius given as 20
Therefore the area = 100 * 40 = 4000
Now the area of the shaded region only= 4000 + \(200\pi\)(semi circle shaded in black) -\(200\pi\)(semi circle shaded in red) = 4000
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Untitled.png [ 55.32 KiB | Viewed 6745 times ]
Re: If each curved side in the figure above is a semicircle with
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04 Feb 2020, 09:55
04 Feb 2020, 09:55
2
No need to do hard calculation. Just Place the lower portion on the upper side. Then it becomes a complete rectangle.
Here, radius = 20, so diameter = 40 which is the width or other side of the rectangle. On the other hand the parallel side = 100.
Then, area of the rectangle = 40 X 100 = 4000.
Ans: B
Here, radius = 20, so diameter = 40 which is the width or other side of the rectangle. On the other hand the parallel side = 100.
Then, area of the rectangle = 40 X 100 = 4000.
Ans: B
