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16 Oct 2017, 01:34
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:07) correct
17%
(00:53)
wrong
based on 71
sessions
History
Date
Time
Result
Not Attempted Yet
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)
Attachment:
2017-10-16_1232.png [ 2.51 KiB | Viewed 6915 times ]
16 Oct 2017, 03:19
Kudos
Bookmarks
Bunuel
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
17 Oct 2017, 11:50
Kudos
Bookmarks
Bunuel
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
