tetris! well actually, thats four. and they're squares. what do your little cubes do?
This is kind of neat. I drew a three dimensional cube. Then divided the faces into 16 squares per face. Then started counting which of those little cubes would have a painted face. I get: 1 red face - 24 cubes 2 red faces - 24 cubes 3 red faces - 8 cubes 4, 5, & 6 red faces - 0 cubes
If you have 5 distinct cubes, the number of arrangements can be calculated using the factorial of the number of cubes. Thus, the total arrangements would be 5! (5 factorial), which equals 120. If the cubes are identical, there would be only 1 arrangement.
8 x 5 - 4 = 36 cubes There is a possibility you mean 8^3 x 5^3 - 4^3 which would be 512 x 125 - 64 = 63936 but that would be "cubed" rather than "cubes."
7/10
The number of cubes in one layer depends on the dimensions of the layer. For example, if the layer is a square with each side measuring 5 cubes, there would be 5 x 5 = 25 cubes in that layer. If the layer has different dimensions, simply multiply the length by the width to find the total number of cubes.
30
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There are 64 such cubes.
Volume is equal to Length x Width x Height. 5x3x2=30 cubes
Draw a three dimensional cube, showing three faces. Divide each face into 6 x 6 =36 squares, representing the faces of the little cubes. Then by inspection it is obvious that no little cube can have more then three painted faces and they will be at the eight corners. Only the edge cubes (not counting the corners) can have two painted faces and there are 48 of then. Finally, only the inner cubes on the surfaces will have one painted face and there are 96 of them. The other 64 cubes are in the inner core and will have no painted surfaces. SO: 6 = 0 ; 5 = 0; 4 =0 ; 3 = 8 ; 2 = 48 ; 1 = 96 . uuuuuu.....
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that depends on how big the ice cubes are, advice: pay attention in class!