Question

a cube of side 5cm is painted on all its faces .If it is sliced into 1 cubic cm , how many 1 cubic cm cubes will have exactly on of their faces painted

Answer 1

If we imagine one of the faces of a 5cm cube, we can easily say that each face would have (5×5)=25 cubes of side 1 cm.

Now, out of these, the boundary cubes on each face would have 2(boundary ones) or 3(corner ones) sides painted. So, on calculating, we have (3×3) =9 cubes on each face with exactly one side painted.

Hence, the answer is 9×6= 45cubes.

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Answer 2

Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.