# Rate of change question about Volume

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.

• What formula are you using for the volume of the vase? It should be a function of the height.
– Jeff
Apr 28, 2014 at 7:25
• @Jeff yes i expressed the volume in terms of h, the height, but i think my expression is wrong. Apr 28, 2014 at 7:36
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– Jeff
Apr 28, 2014 at 16:07

The volume of the vase is $\frac{1}{3}\left(6^2 + (6+\frac{2h}{\sqrt{3}})6 + (6+\frac{2h}{\sqrt{3}})^2 \right)h$.