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AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 4

Lesson 4: Introduction to related rates

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Analyzing related rates problems: expressions

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Consider the following problem:

The radius $r (t)$ ‍ of a cone is increasing at a rate of $3$ ‍ centimeters per second and the height $h (t)$ ‍ of the cone is decreasing at a rate of $4$ ‍ centimeters per second. At a certain instant $t_{0}$ ‍, the radius is $8$ ‍ centimeters and the height is $10$ ‍ centimeters. What is the rate of change of the volume $V (t)$ ‍ of the cone at that instant?

Match each expression with its given value.

	$- 4$ ‍	$3$ ‍	$8$ ‍	$10$ ‍	Not given
$h^{'} (t_{0})$ ‍
$r^{'} (t)$ ‍
$V (t_{0})$ ‍

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