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# How much space, in cubic units, is left vacant when maximum number of

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Math Expert
Joined: 02 Sep 2009
Posts: 64242
How much space, in cubic units, is left vacant when maximum number of  [#permalink]

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01 Nov 2019, 04:54
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Difficulty:

45% (medium)

Question Stats:

65% (01:56) correct 35% (01:48) wrong based on 170 sessions

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How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?

A. 0
B. 36
C. 180
D. 216
E. 384

Are You Up For the Challenge: 700 Level Questions

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Re: How much space, in cubic units, is left vacant when maximum number of  [#permalink]

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01 Nov 2019, 05:12
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Bunuel wrote:
How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?

A. 0
B. 36
C. 180
D. 216
E. 384

Are You Up For the Challenge: 700 Level Questions

Total space = 10x12x16
In any orientation, space used will be 12x16x8
—> Space left out = 12x16x10 - 12x16x8 = 12x16x2 = 384

IMO Option E

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Re: How much space, in cubic units, is left vacant when maximum number of  [#permalink]

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02 Nov 2019, 01:38
Bunuel wrote:
How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?

A. 0
B. 36
C. 180
D. 216
E. 384

Are You Up For the Challenge: 700 Level Questions

total volume of the box ; 12*16*10
total volume of the cube which can fit into the box ; 12*16*8
8 because that is the max dimension of the cube of 4 can cover for space of 10
so ∆ will be 12*16*10- 12*16*8 = 384
IMO E
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Re: How much space, in cubic units, is left vacant when maximum number of  [#permalink]

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24 Jan 2020, 04:49
10*12*16. We will be able to use all of 12 and 16 but only 8 out of 10.

So Area remaining is 2*12*16=384

Option E
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Re: How much space, in cubic units, is left vacant when maximum number of  [#permalink]

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25 Jan 2020, 09:51
Bunuel wrote:
How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?

A. 0
B. 36
C. 180
D. 216
E. 384

Are You Up For the Challenge: 700 Level Questions

The rectangular box is 10 x 12 x 16. For the side length of 10: We can occupy two lengths of 4's. Subtract the two four's and 2 is left.
For the side length of 12: We can occupy the entire area with three 4's.
For the side length of 16: We can occupy the entire area with four 4's.

Imagine the length of 10 as the height, when we fill this box up, we have the entire base of 12 * 16 filled with a height 2 missing. Therefore after filling up the rectangular box, we will just be left with a volume 2 * 12 * 16 left, 2 * 12 * 16 = 384.

(Note this doesn't translate over when two sides are not fully covered, we simply subtract volumes at that point).

Ans: E
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Re: How much space, in cubic units, is left vacant when maximum number of  [#permalink]

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28 Mar 2020, 02:25
Bunuel wrote:
How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?

A. 0
B. 36
C. 180
D. 216
E. 384

Are You Up For the Challenge: 700 Level Questions

Asked: How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?

Total space = 16*12*10
Used space = 16*12*8
Vacant space = 16*12*2 = 384

IMO E
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Re: How much space, in cubic units, is left vacant when maximum number of  [#permalink]

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17 May 2020, 06:00
Let us say the length of the cuboid is 16, width is 12 and height 12... We can keep 4 cubes lenghtwise to fit into 16, 3 cubes alongside the width to fit the 12 but only two cubes alongside the height...so from 10 a height of 2 will be left. So the remaining volume will be 16*12*2= 384
Hence E

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Re: How much space, in cubic units, is left vacant when maximum number of   [#permalink] 17 May 2020, 06:00