Proofs of the Volume of a Sphere.

I was asked to explain why the volume of a sphere is $\frac{4}{3}\pi r^3$ to a student that does not have the knowledge of calculus. In doing so I thought of an argument and I cannot seem to find that argument elsewhere so far. The proofs for the area of the sphere that I know of are:

i) Integrating up spherical shells or direct integration from spherical polar coordinates etc

ii) Cavalieri's Principle

iii) Archimedes proof.

All of which can be found here:https://proofwiki.org/wiki/Volume_of_Sphere

Are there any other proofs out there ? How can I go about finding them ? (Maybe proofs that assume some properties of the sphere, such as its surface area...)