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If each curved side in the figure above is a semicircle with

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If each curved side in the figure above is a semicircle with [#permalink] New post 20 Jun 2018, 09:35
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Attachment:
semi.jpg
semi.jpg [ 30.65 KiB | Viewed 275 times ]


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) \(4,000 - 400\pi\)
[Reveal] Spoiler: OA

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Re: If each curved side in the figure above is a semicircle with [#permalink] New post 23 Jun 2018, 07:37
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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Re: If each curved side in the figure above is a semicircle with   [#permalink] 23 Jun 2018, 07:37
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