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25 Apr 2019, 03:56
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A
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Seven cookies of radius 1 inch are cut from a circle of cookie dough, as shown. Neighboring cookies are tangent, and all except the center cookie are tangent to the edge of the dough. The leftover scrap is reshaped to form another cookie of the same thickness. What is the radius in inches of the scrap cookie?
(A) \(\sqrt{2}\)
(B) 1.5
(C) \(\sqrt{\pi}\)
(D) \(\sqrt{2\pi}\)
(E) \(\pi\)
Attachment:
cca00f7535d16d5f82c2832dbebe7bf865368fed.png [ 24.84 KiB | Viewed 3147 times ]
25 Apr 2019, 04:27
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Area of outer circle=\(pi*3^2=9pi\)
Area of 7 cookies=\(7*pi*1^2=7pi\)
Area of left over=\(2pi\)
Radius=\(\sqrt{2}\)
IMo, Option A.
Area of 7 cookies=\(7*pi*1^2=7pi\)
Area of left over=\(2pi\)
Radius=\(\sqrt{2}\)
IMo, Option A.
eswarchethu135
25 Apr 2019, 04:42
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Each cookie area is \(\pi\)
The larger circle area is \(9\pi\) (radius of the larger circle is 3)
Area of 7 cookies is \(7\pi\)
Scrap area is \(9\pi - 7\pi\)
\(2\pi\)
\(\pi*r^2 = 2\pi\)
\(r = \sqrt{2}\)
OPTION: A
The larger circle area is \(9\pi\) (radius of the larger circle is 3)
Area of 7 cookies is \(7\pi\)
Scrap area is \(9\pi - 7\pi\)
\(2\pi\)
\(\pi*r^2 = 2\pi\)
\(r = \sqrt{2}\)
OPTION: A
