Question

A solid cube of side 12 cm has been painted red, blue and black on pairs of opposite faces. it is then cut into cubical blocks of each side 2 cm. how many cubes have no face painted?

Answer 1

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there are 36 cubes in each layer of 2 cm each. toal 36* 6 layers=216 cubes
in 1st layer and 6th layer, all 36 cubes will be painted from all three sides(top, side and front)
so, 216-72=144 left cubes now
now, out of 144, in each layer(2nd,3rd, 4th,5th), 20 outside cubes of each layer, are painted. so, 
20*4(2nd, 3rd, 4th, 5th)= 80 cubes are still painted(side view and front view of each cube.)
so, remaining cubes are 144- 80=64 cubes are still not painted.