A flower vase, in the form of a hexagonal prism, is to be filled with 512 cubic inches of water. Find the height of the water if the wet portion of the flower vase and its volume are numerically equal.

Question

phi · Answer

By "wet portion" they probably mean the surface area of the vase that is wet.
It will be the "inside" lateral area, plus the area of the bottom.  (but not the area of the top, because there is no top)

phi · Answer

You will need the formulas for:
1) area of a hexagon
2) volume of a prism
3) lateral area of a prism

phi · Answer

I get some ugly cubic equation.  Is it supposed to be this hard?