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23 Nov 2017, 01:21
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D
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Difficulty:
35%
(medium)
Question Stats:
75% (01:40) correct
25%
(02:07)
wrong
based on 33
sessions
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The figure above shows portions of two circles with centers at A and C respectively, and square ABCD with side of length s. What is the perimeter of the curved figure in terms of s?
(A) 4πs/3
(B) 3πs/2
(C) 2πs
(D) 3πs
(E) 4πs
Attachment:
2017-11-23_1215.png [ 7.13 KiB | Viewed 1963 times ]
23 Nov 2017, 02:02
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Answer Choice: D
Required Perimeter = Major Arc BD (circle with center A) + Major Arc BD (circle with center C)
P= 2*\(\pi\)*s*270/360 + 2*\(\pi\)*s*270/360
P= 3\(\pi\)s
Required Perimeter = Major Arc BD (circle with center A) + Major Arc BD (circle with center C)
P= 2*\(\pi\)*s*270/360 + 2*\(\pi\)*s*270/360
P= 3\(\pi\)s
23 Nov 2017, 09:42
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Bunuel
Perimeter = \(\frac{3}{4}\) circumference of one circle * 2
Vertex A of square ABCD = 90°. That 90° "cuts" (shortens) the perimeter of circle with center A by \(\frac{90}{360}=\frac{1}{4}\)
One part of the perimeter of the curved figure hence is \(\frac{3}{4}\) of the circumference of Circle A.
Vertex C of the square does exactly the same thing to the circle with center C.
So perimeter of curved figure =
\(\frac{3}{4}\) circumference of Circle A +
\(\frac{3}{4}\) circumference of Circle C
Radius of both circles = square's side length = \(s\)
Circumference of each circle:\(2πr = 2πs\)
Perimeter of curved figure:
\((2) * (\frac{3}{4} *2πs)=\frac{12πs}{4}=3πs\)
Answer D
