4.5 Solving Related Rates Problems

🎥Watch: AP Calculus AB/BC - Related Rates

The volume of a cone is a special related-rates case because of its two variables that are both rates, radius and height. In a cylinder, the radius is not a problem because it never changes. However, with a cone, as the height changes, the radius will too! Because of this, the VERY FIRST thing you should do when given a cone, is making a proportion between radius and height, and solve for the one that is unneeded to plug it into the volume formula before you do anything else!

Here is an example:

A conical water tank with vertex down has a radius of 8 ft at the top and is 22 ft high. If the water flows into the tank at a rate of 10 ft^3/min,  How fast is the depth of the water increases when the tank is 12 ft deep?

** Remember, always round to 3 decimal places!