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?

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asked Sep 23, 2018 17.3k views

2 Answers

Vladi · Answer 1 · 2018-09-23T11:34:54+0000

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.

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.