1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of the cone. a) By differentiating V = nh with respect to time t, derive an equation that relates h, dh/dt, and dV/dt as the cone shrinks. b) At a certain moment, the height of the cone is decreasing at 2 centimeters per second (cm/sec), and its height is 6 cm. At that same moment, what is the rate of change of the volume of the cone? Do not round your answer. Use the correct unit for your answer. c) At a certain moment, the height of the cone is 8 centimeters, and its volume is decreasing at 160 cm /sec. At that same moment, what is the rate of change of the height of the cone? Do not round your answer. Use the correct unit for your answer.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height
of the cone.
a)
By differentiating V = nh with respect to time t, derive an equation that relates h,
dh/dt, and dV/dt as the cone shrinks.
b)
At a certain moment, the height of the cone is decreasing at 2 centimeters per second
(cm/sec), and its height is 6 cm. At that same moment, what is the rate of change of the
volume of the cone? Do not round your answer. Use the correct unit for your answer.
At a certain moment, the height of the cone is 8 centimeters, and its volume is
c)
decreasing at 160 cm3/sec. At that same moment, what is the rate of change of the height
of the cone? Do not round your answer. Use the correct unit for your answer.
Transcribed Image Text:1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of the cone. a) By differentiating V = nh with respect to time t, derive an equation that relates h, dh/dt, and dV/dt as the cone shrinks. b) At a certain moment, the height of the cone is decreasing at 2 centimeters per second (cm/sec), and its height is 6 cm. At that same moment, what is the rate of change of the volume of the cone? Do not round your answer. Use the correct unit for your answer. At a certain moment, the height of the cone is 8 centimeters, and its volume is c) decreasing at 160 cm3/sec. At that same moment, what is the rate of change of the height of the cone? Do not round your answer. Use the correct unit for your answer.
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