Question

How much of the sphere do you have to paint red so that no matter ow you put a cube in it, some corner touches red?

Answer 1

Explanation:

To achive that you have to piant a ring in red, which will have its big diameter equal to the sphere diameter and its small diameter equal to the cube diagonal.

The diagonal of the cube can be calculated using Pithagoras:

$D^2=L^2+L^2$

Where D is the diagonal and L is the side of the cube