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Chapter 3: Q. 15 (page 299)

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

Short Answer

Expert verified

The derivativesdVdtanddrdtare related bydVdt=2蟺谤丑drdt.

Step by step solution

01

Step 1. Formula used.

The volume of the sphere is given by the formulaV=蟺谤2hcu. units.

02

Step 2. Apply the differentiation.

Given that the radius r, height h, and volume V are functions oft.

Apply the differentiation to V=蟺谤2h with respect to t and keeping h as constant as follows.

role="math" localid="1648728564870" dVdt=2蟺谤丑drdt

03

Step 3. Conclusion.

The derivativesdVdtanddrdtare related bydVdt=2蟺谤丑drdt.

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Most popular questions from this chapter

Restate Rolle鈥檚 Theorem so that its conclusion has to do with tangent lines.

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=ex1+ex

Find the possibility graph of its derivative f'.

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

role="math" localid="1648368106886" f(x)=sin(蟺2x)
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