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A cube is painted red and then cut into 216 little cubes all of the same size how many of the little cubes have 6 red faces 5 red faces 4 red faces 3 red faces 2 red faces 1 red face?
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.....
How many small cubes will have paint on three faces if each cube is 3 inches and painted and cut into 27 smaller cubes that are 1 inch on each side?
Answer = 8. The only small cubes with paint on three faces are those that occupied the corners of the original cube.
A cube is painted red and then cut into 64 little cubes all of the same size how many of the little cubes have 6 red faces 5 red faces 4 red faces 3 red faces 2 red faces 1 red face?
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
A rectangular solid is painted and then sliced into 54 cubes how many of the resulting cubes have no faces painted one face painted two faces painted three faces painted?
It depends on how the rectangular solid is built. If the side of a cube is "a", then your original solid could be a x a x 54a, or a x 2a x 27a, or 2a x 3a x 9a or one of quite a few others, and the answer depends on the one you specify.
A cube is painted red and cut into 64 cubes how many have 6 red faces 5 red faces 4 red faces 3 red faces 2 red faces 1 red face?
There would be 8 will 3 faces painted red, 24 with 2 faces painted red, 24 with 1 face painted red, and 8 that have no faces painted red.
