A sphere of radius r inside a cube touches each one of the six sides of the cube what is the volume of the cube in terms of r?

Answer 1

2r3, because if you have a radius touching all six sides, you could then double this to get the diameter of the sphere, which would be 2r, then this would be, being a cube, the length of every edge of the cube, which we cube or put to the 3rd power, to find volume.