Bunuel wrote:
Official Solution:
What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?
A. 12
B. 18
C. 20
D. 24
E. 30
The 12x16 floor can be covered with 12 cubes. Another 12 cubes will form the second layer. The height of this construction will be 8; the box won't accommodate any more cubes.
Answer: D
How do we know that that the floor is 10x16 and it is not 12x16?
I am asking because since we are not told which value corresponds to l,w,h, then I would think that we need to use the volume, which does not require you to know which of the values is l,w or h.
In this sense, why isn't it volume of rectangular box 10x12x16 = 1920 divided by surface area of the cube 6*16= 96, which gives 20?
At first I thought of using the volume for the cube as well, but what we need to know is its outside area, right? So, the space it would assume inside the box.
Now, what I am not sure about is whether we also need to match each of the l,w,h of the square with those of the box. In this case though, shouldn't we be told specifically which value corresponds to l,w,h?