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If each curved side in the figure above is a semicircle with radius 20

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If each curved side in the figure above is a semicircle with radius 20 [#permalink]

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New post 16 Nov 2017, 01:49
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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 region by the above figure?

(A) 2,000
(B) 4,000
(C) 2000 – 200π
(D) 4,000 – 200π
(E) 4000 – 400 π

[Reveal] Spoiler:
Attachment:
2017-11-16_1237.png
2017-11-16_1237.png [ 3.19 KiB | Viewed 419 times ]
[Reveal] Spoiler: OA

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Re: If each curved side in the figure above is a semicircle with radius 20 [#permalink]

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New post 16 Nov 2017, 04:32
B.
area of the rectangle is = 40*100 = 4000
area of semicircle is = 1/2 * pi*20*20 = 200pi
now, area of the entire thing is = 4000-200pi+200pi = 4000
hence, B.

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Re: If each curved side in the figure above is a semicircle with radius 20 [#permalink]

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New post 16 Nov 2017, 09:02
observe the figure ,
below semi circle is equal to semi circle cut out above ( r is equal)
only find the area of rectangle 40*100 = 4000
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If each curved side in the figure above is a semicircle with radius 20 [#permalink]

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New post 16 Nov 2017, 09:10
The answer should be 4000 (A) Width is 2R= 20*2

area of rectangle L*B= 100*40= 4000. Now a semi circle is inside the rectangle and one is outside where both have same radius so each cancels out and the area of the figure is 4000.

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Re: If each curved side in the figure above is a semicircle with radius 20 [#permalink]

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New post 17 Nov 2017, 14:33
Bunuel wrote:
Image
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 region by the above figure?

(A) 2,000
(B) 4,000
(C) 2000 – 200π
(D) 4,000 – 200π
(E) 4000 – 400 π

[Reveal] Spoiler:
Attachment:
2017-11-16_1237.png


We will use a method called “cut and paste.” We see that we can cut the bottom semicircle out and paste it to the top so that the entire figure becomes a rectangle. The length of the rectangle will be 100 and the width will be the diameter or the semicircle, which is 40. Thus, the area of the rectangle, or the figure, is 100 x 40 = 4,000.

Answer: B
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Re: If each curved side in the figure above is a semicircle with radius 20   [#permalink] 17 Nov 2017, 14:33
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