Fish Tank Problem - Animated
- David Gurney
Use the sliders to change the length and width of the tank, and also to change the inflow rate, i.e. the rate of flow of water into the tank. The length and width are in feet. The inflow rate is in cubic feet per minute.
The key point in doing these problems is to remember that rates can be thought of as derivatives. In this case, the inflow rate is the derivative of volume with respect to time, and the rate at which the height is increasing is the derivative of height with respect to time. Also note that the final answer comes from dividing the inflow rate by the product of the length times the width. Thus, the units are cubic feet per minute divided by feet squared, which results in feet per minute - reasonable units for rate of change of the height.