Question

When slicing a cube perpendicular to its base, parallel to its base, or diagonal to its base, what is the maximum number of sides the cross section shape could have?

Answer 1

The maximum number of sides a cross-sectional shape of a cube can have is 6, occurring when the cube is sliced diagonally through opposite edges.

Step-by-step explanation:

When slicing a cube, the maximum number of sides that the cross-sectional shape could have depends on the orientation of the slice:

• If sliced perpendicular to its base, the cross section is a square with 4 sides.
• If sliced parallel to its base, the cross section is also a square with 4 sides.
• When sliced diagonally (along a plane that intersects the opposite edges of the cube), the cross section can be a hexagon with a maximum of 6 sides.

Therefore, the maximum number of sides a cross section can have when slicing a cube is 6, which occurs with a diagonal cut through the cube.

Answer 2

5 sides, slicing it diagonally will turn it into a triangular prism