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Unit 4

4.5 Solving Related Rates Problems

1 min readโ€ขjune 8, 2020

Meghan Dwyer


๐ŸŽฅWatch: AP Calculus AB/BC - Related Rates

Resources:

Special Example: Volume of a Cone ๐Ÿฆ

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,ย  How fast is the depth of the water increases when the tank is 12 ft deep?

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https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(492).png?alt=media&token=2e8ca6a2-33e8-461b-9bca-1df1501d4ce8

** Remember, always round to 3 decimal places!

Resources:

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