Question

A cube is dissected by one plane at \( \frac{1}{6} \) side length and one plane at \( \frac{1}{2} \) side length in each of the three dimensions of \(xy\), \(yz\), and \(xz\). How many cubes will be formed after dissecting the large cube?

Hint:

When dividing a 3D shape like a cube, each plane adds one division along that dimension. Multiply the number of divisions for all dimensions to get the total number of resulting shapes.

Answer 1

1. Each plane divides the cube into multiple sections along the given dimension.
2. With the given dimensions, the large cube is divided into 3 parts in total: one along \( \frac{1}{6} \), one along \( \frac{1}{2} \), and one remaining piece.
Conclusion: The cube is divided into 3 smaller cubes.