# Homework Help: Show by using Torricelli's law

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1. Nov 21, 2016

### xaxa

• Member warned that the homework template must be used
A cone-shaped water tank is given by $$V(h)=\pi(h-\frac{h^2}{3}+\frac{h^3}{27})$$

Show using Torricelli's law law that $$-2\sqrt2\pi(\frac{1}{\sqrt{h}}-\frac{2}{3}\sqrt h+\frac{1}{9}h^{3/2})\frac{dh}{dt}=1$$

What I have done so far: $$V'=\frac{1}{9}\pi(h-3)^2h'$$

2. Nov 21, 2016

### haruspex

There must be more to the question statement. The given formula for V only tells you something about the shape of the vessel. The thing to be proved has the depth varying with time. Is there fluid flowing in? Out? Through what orifice?