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# Two crystal spheres of diameter x/2 are being packed in a cubic box wi

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Math Expert
Joined: 02 Sep 2009
Posts: 45360
Two crystal spheres of diameter x/2 are being packed in a cubic box wi [#permalink]

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05 Feb 2018, 06:32
00:00

Difficulty:

75% (hard)

Question Stats:

38% (01:42) correct 62% (01:55) wrong based on 21 sessions

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Two crystal spheres of diameter x/2 are being packed in a cubic box with a side of x. If the crystal spheres are in the box and the rest of the box is completely filled with packing powder, approximately what proportion of the box is filled with packing powder? (The volume of a sphere of radius r is $$\frac{4}{3}*\pi r^3$$.)

(A) 17/16
(B) 1/8
(C) 1/2
(D) 3/4
(E) 7/8

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Re: Two crystal spheres of diameter x/2 are being packed in a cubic box wi [#permalink]

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05 Feb 2018, 09:43
Volume of the cube = x^3

Total volume of the 2 crystal spheres = 4/3 * pi * (x/4)^3 = pi * (x^3)/24 = (x^3)/8

Volume occupied by the packing powder = x^3 - (x^3)/8 = 7(x^3)/8

Proportion occupied by packing powder = Volume occupied by the packing powder/Volume of the cube = 7/8

Re: Two crystal spheres of diameter x/2 are being packed in a cubic box wi   [#permalink] 05 Feb 2018, 09:43
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