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A window has the shape of a semicircle placed on top of a square. If

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A window has the shape of a semicircle placed on top of a square. If [#permalink]

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A window has the shape of a semicircle placed on top of a square. If the length of a side of the square is 20 inches, how many square inches is the area of the window?

(A) 400
(B) 200π
(C) 50(8 + π)
(D) 200(2 + π)
(E) 400(1 + π)


[Reveal] Spoiler:
Attachment:
2017-10-16_1232.png
2017-10-16_1232.png [ 2.51 KiB | Viewed 562 times ]
[Reveal] Spoiler: OA

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A window has the shape of a semicircle placed on top of a square. If [#permalink]

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New post 16 Oct 2017, 02:19
Bunuel wrote:
Image
A window has the shape of a semicircle placed on top of a square. If the length of a side of the square is 20 inches, how many square inches is the area of the window?

(A) 400
(B) 200π
(C) 50(8 + π)
(D) 200(2 + π)
(E) 400(1 + π)


[Reveal] Spoiler:
Attachment:
2017-10-16_1232.png

The area of the window = area of square + area of semicircle.

Area of square = \(s^2 = 20^2 = 400\)

Area of semicircle = \(\frac{\pi*r^2}{2}\)

The diameter of the semicircle is the side of the square, which = 20
\(d = 2r\)
\(20 = 2r\)
\(r = 10\)

Semicircle area: \(\frac{\pi*100}{2} = 50\pi\)

Area of window =

\(400 + 50\pi\), factor out 50 =

50(8 + π)

Answer
[Reveal] Spoiler:
C

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Re: A window has the shape of a semicircle placed on top of a square. If [#permalink]

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New post 17 Oct 2017, 10:50
Bunuel wrote:
Image
A window has the shape of a semicircle placed on top of a square. If the length of a side of the square is 20 inches, how many square inches is the area of the window?

(A) 400
(B) 200π
(C) 50(8 + π)
(D) 200(2 + π)
(E) 400(1 + π)


[Reveal] Spoiler:
Attachment:
2017-10-16_1232.png


Since the length of the square is 20 inches, the diameter of the circle is 20 inches, so the area of the semicircle is 1/2 x π x 10^2 = 50π inches^2.

The area of the square is 20 x 20 = 400 inches^2.

So, the total area of the window is:

50π + 400 = 50(π + 8)

Answer: C
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Re: A window has the shape of a semicircle placed on top of a square. If [#permalink]

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New post 22 Oct 2017, 14:16
Here we go, area of the square is 20^2=400
-For the semicircle, we're given the diameter is 20. R=20/2=10.
-Area of a circle with radius of 10 is 10^2π=100π, divide by 2 since it's a semicircle and get 50π
400+50π, is not an answer, but if we factor out 50, we get 50(8+π), C.
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Re: A window has the shape of a semicircle placed on top of a square. If   [#permalink] 22 Oct 2017, 14:16
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