"The radius of the base of a cylinder is decreasing at a rate of 12 kilometers per second. The height of the cylinder is 2.5 kilometers. At a certain instant, the radius is 40 kilometers. What is the rate of change of the volume of the cylinder at that instant (in cubic kilometers per second)?"
"The radius of the base of a cylinder is decreasing at a rate of 12 kilometers per second. The height of the cylinder is 2.5 kilometers. At a certain instant, the radius is 40 kilometers. What is the rate of change of the volume of the cylinder at that instant (in cubic kilometers per second)?"
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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"The radius of the base of a cylinder is decreasing at a rate of 12 kilometers per second.
The height of the cylinder is 2.5 kilometers.
At a certain instant, the radius is 40 kilometers.
What is the rate of change of the volume of the cylinder at that instant (in cubic kilometers per second)?"
For this kind of problem, do I just plug in "h" or do I find dh/dt? If I'm not told a value is changing, do I just plug it in, rather than use the derivative, dh/dt?
dv/dt = h * pi*2r*(dr/dt)
or
dv/dt = dh/dt *pi*2r*(dr/dt)
Summary: How do I know which values need to be derivatives when solving for another derivative?
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