A cube is sliced into halves in such a way that the cut is a regular hexagon. What is the angle (in degrees) between the plane of the cut and the base of the cube?
What is the side length of the smallest regular hexagon that can pack 6 circles of unit length in the given way?
A unit sphere (radius = 1) is out on a flat plane in the rain. Find the side length of the largest cube that can hide underneath it and not get wet.
The ratio between the exterior angle and the interior angle of a regular polygon is 2 : 3 .
Find the number of sides of the polygon.
Visualize a cube. You know it has 6 faces, 8 corners, and 12 edges. Now, imagine a knife slicing away each corner with a straight plane cut. How many total edges are there now?