5. What is the least possible number of cuts required to cut a cube into 64 identical pieces?

1. A. 8
2. B. 9
3. C. 12
4. D. 16

Answer: B

Explanation

To cut a cube into `N` identical pieces, where `N = x * y * z`, the minimum number of cuts required is `(x-1) + (y-1) + (z-1)`. For identical pieces, `x = y = z`. In this case, `N = 64`. So, we need to find the cube root of 64, which is 4 (since 4 * 4 * 4 = 64). This means the cube needs to be divided into 4 segments along each of its three dimensions. The number of cuts required along each dimension is `(4-1) = 3`. Since there are three dimensions (length, width, and height), the total minimum number of cuts required is `3 + 3 + 3 = 9`. This is a standard problem testing spatial reasoning and basic geometric understanding.