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# Analyzing related rates problems: expressions

AP.CALC: CHA‑3 (EU), CHA‑3.D (LO), CHA‑3.D.1 (EK), CHA‑3.D.2 (EK)

## Problem

Consider the following problem:
The radius r, left parenthesis, t, right parenthesis of a cone is increasing at a rate of 3 centimeters per second and the height h, left parenthesis, t, right parenthesis of the cone is decreasing at a rate of 4 centimeters per second. At a certain instant t, start subscript, 0, end subscript, the radius is 8 centimeters and the height is 10 centimeters. What is the rate of change of the volume V, left parenthesis, t, right parenthesis of the cone at that instant?
Match each expression with its given value.

minus, 4
3
8
10
Not given
h, prime, left parenthesis, t, start subscript, 0, end subscript, right parenthesis
r, prime, left parenthesis, t, right parenthesis
V, left parenthesis, t, start subscript, 0, end subscript, right parenthesis
Stuck?
Stuck?