A 4x4x4 cubical box contains sixty-four identical small cubes that exactly fill the box. How many of these small cubes touch a side or the bottom of the box?
2006-12-29 04:24:44 · 12 answers · asked by gear head 1 in Science & Mathematics ➔ Mathematics
Thanks all for your answers. This is what me and my daughter came up with. We figured all the squares but the center 8 touch a side or bottom of the cube which gave us the answer of 56 cubes.
2006-12-29 05:05:14 · update #1
All but 8, I think...
addendum*: 'all but 8' means 'all but 8', i.e: 'all 64 bar 8', which makes Twang (the latecomer many posts down) a bit of an idiot...
*I like that word (addendum), don't you? Is it spelt correctly? Is 'spelt' correctly spelled?
2006-12-29 04:28:02 · answer #1 · answered by K V 3 · 2⤊ 0⤋
I've got a slightly different take on this one.
There are 4 layers of 16 boxes.
All of the bottom 16 touch the bottom.
12 of the next 3 layers touch the sides.
Therefore, 16 + 3*12= 52 boxes either touch the bottom or sides.
I would agree with 56 if the question asked for touching a side, the bottom, or the top.
2006-12-29 04:40:26 · answer #2 · answered by bkc99xx 6 · 1⤊ 0⤋
No, KV is not right, but he has the right idea. The inside of the 4x4x4 cube that does not touch any side is a 2x2x2, or 8 cubes. However, you must subtract 8 from 64 to get the actual answer you are looking for, the number of sides that do touch the box.
64-8=56
So there are 56 cubes touching the sides.
2006-12-29 04:34:58 · answer #3 · answered by Twang 2 · 0⤊ 2⤋
Pandora's Box
2016-03-28 23:46:41 · answer #4 · answered by Anonymous · 0⤊ 0⤋
The big box would contain 4 layers of 4 small boxes each.
The four each in the upper and lower layers, plus three times four would touch in each of the two remaining layers.
16 x 2 + 4 x 3 x 2 = 56
2006-12-29 04:42:51 · answer #5 · answered by Anonymous · 0⤊ 0⤋
52 of them....
there are 4 on an edge, so 2 opposite faces = 16 * 2 = 32
Now the 2 other sides also have 16, but we've already counted 8 of them each = 2 * 8 = 16
Finally, there's only 4 on the bottom we haven't counted = 4
32 + 16 + 4 = 52
2006-12-29 04:49:52 · answer #6 · answered by TankAnswer 4 · 0⤊ 0⤋
56
2006-12-29 04:32:29 · answer #7 · answered by Anonymous · 0⤊ 0⤋
the no of boxes touch bottom is 16.
the volume of the big box is 64. Hence only 64 small boxes can fit.
The bottom area is 16.
2006-12-29 04:47:29 · answer #8 · answered by Suhas 2 · 0⤊ 0⤋
If the top isn't considered a side, then it would be 64-(2*2*3) =
64-12 = 52.
2006-12-29 04:42:07 · answer #9 · answered by yljacktt 5 · 0⤊ 0⤋
KV is right. Think about the "inner" cube of cubes that do not touch the side. It is a 2x2x2 box!
2006-12-29 04:30:52 · answer #10 · answered by firefly 6 · 0⤊ 0⤋