



 
Hi Tracy. 1) Find the relationship between the quantities. The involved quantities are volume and height in your question. So we turn to the equation for the volume of a cone: V = 1/3 (pi) r^{2} h. Since the radius of the base always equals half the height, we have r = (h/2), so the equation for the volume becomes V = h^{3} / 12. 2) Differentiate the equation with respect to time. This will relate the rates. This means you differentiate both sides of the equation: dV/dt = d(h^{3}/12)/dt dV/dt = (1/12) d(h^{3})/dt dV/dt = 3h^{2}/12 (dh/dt) < remember that the chain rule applies! dV/dt = h^{2} / 4 (dh/dt) 3) Substitute in the values you know are given in the question. dV/dt is the rate of change of the volume. That's 10 cubic feet/minute. h is the height: 5 ft. dh/dt is the rate of change of the height, which is what you are asked for. So we simply plug them in and solve for dh/dt: 10 = 5^{2} / 4 (dh/dt) dh/dt = 40 / 25 dh/dt = 1.6 ft / minute Hope this helps. In the future, let us know where you are stuck on a problem, rather than just sending the question.  


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