Main content

AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 4

Lesson 4: Introduction to related rates

Analyzing related rates problems: equations

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

Zhenghao was given this problem:

The radius r, left parenthesis, t, right parenthesis of a sphere is decreasing at a rate of 1 meter per hour. At a certain instant t, start subscript, 0, end subscript, the radius is 4 meters. What is the rate of change of the volume V, left parenthesis, t, right parenthesis of the sphere at that instant?

Which equation should Zhenghao use to solve the problem?

(Choice A)
V, left parenthesis, t, right parenthesis, equals, 2, pi, dot, r, left parenthesis, t, right parenthesis
(Choice B)
V, left parenthesis, t, right parenthesis, equals, pi, open bracket, r, left parenthesis, t, right parenthesis, close bracket, squared
(Choice C)
V, left parenthesis, t, right parenthesis, equals, 4, pi, open bracket, r, left parenthesis, t, right parenthesis, close bracket, squared
(Choice D)
V, left parenthesis, t, right parenthesis, equals, start fraction, 4, divided by, 3, end fraction, pi, open bracket, r, left parenthesis, t, right parenthesis, close bracket, cubed

Stuck?

AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 4

Problem