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A cube of side 8 cm is painted red on all the sides. It is then cut into smaller, each of side 2 cm. How many of these smaller cubes have one or more sides painted red?

Question

A cube of side 8 cm is painted red on all the sides. It is then cut into smaller, each of side 2 cm. How many of these smaller cubes have one or more sides painted red?

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Solution

Step 1: Determine the number of smaller cubes

The cube of side 8 cm is cut into smaller cubes of side 2 cm. The number of smaller cubes can be calculated by cubing the ratio of the larger cube's side to the smaller cube's side.

So, (8 cm / 2 cm) ^ 3 = 4^3 = 64 smaller cubes.

Step 2: Determine the number of smaller cubes with no sides painted

The smaller cubes that are inside the larger cube and do not touch any of the larger cube's sides will have no sides painted. These cubes form a smaller cube inside the larger cube, with side length 2 cubes less than the larger cube.

So, (4 cubes - 2 cubes) ^ 3 = 2^3 = 8 smaller cubes have no sides painted.

Step 3: Determine the number of smaller cubes with one or more sides painted

Subtract the number of smaller cubes with no sides painted from the total number of smaller cubes.

So, 64 total cubes - 8 cubes with no sides painted = 56 cubes have one or more sides painted red.

This problem has been solved

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