Question 46

A cuboid of dimensions $$(8 cm. \times  6 cm. \times 5 cm.)$$ is painted RED on the pair of opposite surfaces of dimensions $$(8 cm. \times 6 cm.)$$. Remaining two opposite surfaces of dimensions $$(8cm. \times 5 cm.)$$ are painted BLACK. And two surfaces of dimensions $$(6 cm. \times 5 cm.)$$ are painted with BLUE colors. Now the block is divided among smaller cubes of dimensions $$(1 cm. \times 1 cm. \times 1 cm.)$$. In how many of the small cubes all the three colors appear?

Solution

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Since the opposite faces are painted with the same color, The area where all 3 colors will be present is the corners. Since there are 8 corners of the cube. After cutting there will be 8 cubes with 3 colors on the faces 

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