What structure encloses the most space with the least surface area (has the the highest volume to surface area ratio) ?

That structure would be the Sphere.

With a Volume of V = 4/3*π*r**3

And a surface area of A = 4*π*r**2

r = (A / (4*π)) * * 1/2

V = 4/3*π * [A^ (3/2) / (8 π^ (3/2)) ] = A^ (3/2) / (6 sqrt (π))

We can graph V in tems of A

And compare it to the graph y = x

We can see that the Volume increases more rapidly compared to the Area