Related Rates – Draining a Cone

This related-rates example demonstrates how to set up and solve a problem involving draining a conical (cone-shaped) tank using calculus. This is specifically an inverted cone with the water level dropping at a constant rate, and we are trying to compute the rate at which water is training from the tank for a specific depth. We follow the steps:

1. Draw a picture and identify all quantities.
2. Write an equation that relates the various quantities of the exercise. If necessary, use geometry to eliminate a variable.
3. Use the Chain Rule to differentiate both sides with respect to t.
4. Substitute known values and solve for the desired quantity.
5. Check that the answer is reasonable.

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