A large vase has a square base of side length $6 \text{ cm}$, and flat sides slopingoutwards at an angle of $120^{\circ}$ with the base. Water is flowing in at $12 \text{ cm}^3/\text{s}$. Find, to three significant figures, the rate at which the height of water is rising when the water has been flowing in for $3$ seconds.
Spent around an hour trying to do it, but I keep getting the answer wrong. I think I'm not getting the right volume function.
The volume of the vase is $\frac{1}{3}\left(6^2 + (6+\frac{2h}{\sqrt{3}})6 + (6+\frac{2h}{\sqrt{3}})^2 \right)h$.