Express the volume of a sphere as a percentage of the volume of the smallest cube that can completely envelop the sphere

Answer 1

The smallest cube that can completely envelope a sphere will have have it's side equal to the diameter of the the sphere.

So, if radius of sphere =r, volume is 4/3*π* r³

Volume of cube is (2r)³

Therefore, percentage=100*( 4/3*π* r³)/(2r)³= 50π/3=52.38%