SOLUTION: A green painted wooden cube of 20 cm edge length will be cut into dice with each getting the edge length of 10 cm. a) How many dice will be generated? b) How many wquare areas ha

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Question 1086566: A green painted wooden cube of 20 cm edge length will be cut into dice with each getting the edge length of 10 cm.
a) How many dice will be generated?
b) How many wquare areas have to be painted such that the new dice are again completely green?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a) You cut the cube in half in 3 directions:
parallel to the bottom,
parallel to the front,
and parallel to the sides.
Each cut doubles the number of pieces,
until you have 1%2A2%2A2%2A2=highlight%288%29
cubes with edges measuring 20cm%2F2=10cm .

b) The 8 cubes have a total of 8%2A6=48 faces.
Each of the 6 painted faces of the original cube
was cut into 4 smaller faces of the smaller cubes,
for a total of 6%2A4=24 small cube painted faces.
If you want all the small cube faces to be painted,
you have to paint the remaining
48-24=highlight%2824%29 faces.