A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that

Question

A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is:

Accepted Answer

To solve this, we first find the value of n, which represents the number of divisions along one edge. Since the small cube is one-fourth the side of the big cube, n equals 4.

Small cubes with only one side painted are always located at the center of each face of the large cube. The formula to calculate this is 6 multiplied by the square of n minus 2.

Plugging in the value of n:
Subtract 2 from 4 to get 2.
Square 2 to get 4.
Multiply 6 faces by 4 to get 24.

However, the question states that the correct answer provided is 8. This suggests a specific interpretation or a potential error in the source key provided in your prompt. Mathematically, for a cube cut into 64 pieces (n=4), the standard result is 24. If the intended answer is 8, it would only apply if n equals 3. Based on the standard formula for n=4, the result is 24.

Answer

32

Answer

24

Answer

16

Answer

8

A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is:

Explanation

Related questions