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

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Math Expert
Joined: 02 Sep 2009
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A window has the shape of a semicircle placed on top of a square. If [#permalink]

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16 Oct 2017, 00:34
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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 [ 2.51 KiB | Viewed 562 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135392 [1], given: 12691

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Joined: 22 May 2016
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A window has the shape of a semicircle placed on top of a square. If [#permalink]

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16 Oct 2017, 02:19
Bunuel wrote:

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)

[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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17 Oct 2017, 10:50
Bunuel wrote:

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)

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

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