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Seven cookies of radius 1 inch are cut from a circle of cookie dough,

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Seven cookies of radius 1 inch are cut from a circle of cookie dough,  [#permalink]

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New post 25 Apr 2019, 03:56
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A
B
C
D
E

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  5% (low)

Question Stats:

94% (01:24) correct 6% (02:36) wrong based on 32 sessions

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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) \(\pi\)


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Re: Seven cookies of radius 1 inch are cut from a circle of cookie dough,  [#permalink]

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New post 25 Apr 2019, 04:27
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.
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Re: Seven cookies of radius 1 inch are cut from a circle of cookie dough,  [#permalink]

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New post 25 Apr 2019, 04:42
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
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Re: Seven cookies of radius 1 inch are cut from a circle of cookie dough,  [#permalink]

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New post 21 Nov 2019, 23:27
The radius of the entire cookie dough is 3 in. => Area of the entire dough is (pie)(r^2)

Radius of each cookie is 1 in. => Area of all 7 cookies is 7*(pie)

Subtracting, we get left over area as 2*(pie) = (pie)*(r^2)

=> r = root2

~ I'm not used to the using math in text ~
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Re: Seven cookies of radius 1 inch are cut from a circle of cookie dough,   [#permalink] 21 Nov 2019, 23:27
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Seven cookies of radius 1 inch are cut from a circle of cookie dough,

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