Question 1208651
If we try to solve for h, we can expand the right hand side and get {{{V=160sqrt(6)*h*sqrt(h)-24.28h^2}}}. Letting {{{a=sqrt(h)}}} gives {{{-24.28a^4+160sqrt(6)*a^3-V=0}}}.
Although it is theoretically possible to isolate h using the quartic formula, that would be incredibly tedious and likely impossible without the help of a computer.