How can I prove that the following problem is NP-complete?

I have an spheric container in which I have to introduce n identical spheres. All of the little spheres have to be into the container and they can’t overlap each other. The idea is to minimize the container’s ratio.

I know that this is a packing problem but is three-dimensional so I don’t know how to prove that it’s a NP-complete problem. Can you help me?