AP Calculus AB – Related Rates 

Students that are taking AP Calculus (or any Calculus course) usually find related rates word problems to be difficult. The concept however is really not so hard to understand. The idea is that you have two or more quantities that are changing with time, and those two quantities are related in some way. In a Precalculus problem, we would explore the relationship between those two quantities. But in a Calculus problem we explore the relationship between the rates at which those quantities are changing.

Let’s try a typical AP Calculus AB related rates problem (note that any Calculus AB problem can also appear on the BC exam). I will provide a full explanation for this problem tomorrow. In the meantime, feel free to leave your own solutions in the comments.

Level 4 Related Rates Problem

The radius of a spherical balloon is decreasing at a constant rate of 0.5 centimeters per second. At the instant when the volume V becomes 288π cubic centimeters, what is the rate of decrease, in square centimeters per second, of the surface area of the balloon?

(A) 24π
(B) 48π
(C) 64π
(D) 72π

More AP Calculus Problems with Explanations

If you are preparing for one of the AP Calculus exams, you may want to take a look at one of the following books.

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