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Chapter 3: Q. 16 (page 299)

Suppose the radius r, height h, and volume V of a cylinder are functions of time t. How is dVdt related todhdt if the radius of the cylinder is constant?

Short Answer

Expert verified

The derivatives dVdtand dhdtare related bydVdt=蟺谤2dhdt.

Step by step solution

01

Step 1. Formula used.

The volume of the cylinder is given by the formula V=蟺谤2hcu. units.

02

Step 2. Apply the differentiation.

Apply the differentiation to V with respect to t and keeping ras constant as follows.

ddtV=ddt蟺谤2hdVdt=蟺谤2dhdt

03

Step 3. Conclusion.

The derivativesdVdtanddhdtare related bydVdt=蟺谤2dhdt.

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Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

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