capacitance of a body versus capacitance of inscribed and circumscribed spheres

bhh1988

just out of curiosity - it seems evident to me that the capacitance of a conductive body should be between the capacitance of an inscribed sphere and the capacitance of a circumscribed sphere. But I can't figure out how to prove this.

If you prove this, it follows that the energy required to assemble a charge distribution of some conductor is between the energy required to assemble a circumscribed sphere of the same potential and an inscribed sphere of the same potential (or of the same total amount of charge).