A cube has edges that are s centimetres in length. Identical : PS Archive
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# A cube has edges that are s centimetres in length. Identical

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A cube has edges that are s centimetres in length. Identical [#permalink]

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13 Sep 2006, 02:23
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A cube has edges that are s centimetres in length. Identical square holes, centred in each face of the cube, are cut through to the opposite sides of the cube and the volume of the resulting solid, shown above, is p% of that of the original cube. If the holes are t centimetres wide and s=kt where k>1, then what is p in terms of k?

(A) 100-(2k^3-3)*100/k (B) 100-(3k-2)*100/k^3 (C) 100- (2k-3)*100/k^3
(D) 100-(2k-3)*100/k^2 (E) 100-(k^3-2)*100/k^3
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13 Sep 2006, 02:53
Get (B)

Volume Cube = s^3
Volume removed = 3*t^2*s-2*t^3

Thus,
p/100*Volume Cube = Volume Cube - Volume removed
<=> p/100*s^3 = s^3 - 3*t^2*s+2*t^3
<=> p = 100 - 100*(3*(t/s)^2 - 2*(t/s)^3)

Since, k = s/t

p= 100 - 100*(3*k - 2)/k^3
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