A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted? Correct Answer 54
Imagine just one face of the 5×5 cube. Which of the 1×1 cubes will have paint on only one face? Only those which are not on the edges - these will share a painted face with another side. The cubes that are not part of the edge form a 3×3 grouping of 1 cm cube.Therefore each face has 9 cubes that are painted one color.Since there are 6 faces we get 6×9 = 54