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solid geometry

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by quantskillsgmat » Sat Dec 24, 2011 9:45 pm
If cuboids of dimension 4x6x8 are joined to form a cube.how many cuboids are needed to make smallest possible cube having integer side.
a)20
b)24
c)13
d)16
e)none
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by shankar.ashwin » Sat Dec 24, 2011 10:54 pm
I believe the length of the bigger cube would be the LCM of the 3 numbers/dimensions 24

Now volume of both the figures should be the same.

So, x * (4*6)*8 = 24^3

x = 72. None of the above choices IMO.
Last edited by shankar.ashwin on Sun Dec 25, 2011 6:04 am, edited 1 time in total.
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by pemdas » Sun Dec 25, 2011 12:35 am
del.
quantskillsgmat wrote:If cuboids of dimension 4x6x8 are joined to form a cube.how many cuboids are needed to make smallest possible cube having integer side.
a)20
b)24
c)13
d)16
e)none
Last edited by pemdas on Sun Dec 25, 2011 7:46 am, edited 1 time in total.
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by user123321 » Sun Dec 25, 2011 6:40 am
I agree with Ashwin on this. As final length of cube should be LCM of those 3 numbers.
so we have 24*24*24 cube and for that we need...
(24*24*24)/4*6*8 = 6*4*3 = 72 cuboids

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by pemdas » Sun Dec 25, 2011 7:45 am
i think you are guys right, as I haven't accounted for the internal face

so the answer is e?
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