Water Tank Rate of Change Problem: Find the Rate at Which Water Level is Rising

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Homework Statement



A water tank is built in the shape of a circular cone with a height of 6 m and a diameter of 10 m at the top. Water is being pumped into the tank at a rate of 2m^{3}
per minute. Find the rate at which the water level is rising when the water is 2 m deep.

Homework Equations



Volume of a cone - \frac{1}{3} \Pi r^{2} h

Surface area of a cone - \Pi r s + \Pi r^{2}

The Attempt at a Solution



\frac{dV}{dt} = 2m^{3}/min

I think I have to find \frac{dh}{dt} but other than that I'm completely lost.
 
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what is h as a function of v?
 
I'm not sure I understand.
 
Can you relate r and h with the knowledge that the tank is a cone?
 
What both ice109 and TMM are trying to say is that you have two variables since

V = \frac{1}{3}{\pi}r^2h

Both the radius and height are effecting the volume. So before you can find dh/dt you need to find a way to relate r in terms of h.
 
Draw a triangle, vertex at the bottom, base horizontal, with height 6 and base length 10, representing the water tank. Draw a horizontal line representing the water line in the tank, with length 2r (since the diameter is twice the radius) and height above the vertex h. Use "similar triangles" to connect h and r.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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