Couldn't really put the constraints on the formula for surface area of a cone.If you fit the cone with the largest possible surface area (lateral area plus area of base) into a sphere, what percent of the volume of the sphere is occupied by the cone

So:

$V(sphere) = \dfrac{4}{3}\pi r^3$

I guess I could just take $r = 1$ then it is: $V(sphere) = \dfrac{4}{3} \pi$

$ A(cone)= \pi r (r + \sqrt{h^2 + r^2}) $

And here we have to define the domain, as I understand; so $ r \leq 1$, $h \leq 2r$

Is this correct thinking?