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Chapter 3: Q. 22 (page 299)

In Exercises 19鈥�26, write down an equation that relates the two quantities described. Then use implicit differentiation to obtain a relationship between the rates at which the quantities change over time.

The volume V and radius r of a cylinder with a fixed height of 10 units.

Short Answer

Expert verified

The equation that relates the volume Vand the radius r of the cylinder is V=10蟺谤2.

The derivativedVdtanddrdtare related by dVdt=20蟺谤drdt.

Step by step solution

01

Step 1. Given information.

The height of a cylinder is 10 units.

02

Step 2. Formula used.

The volume of a cylinder is V=蟺谤2hcu. units.

03

Step 3. Apply the value of h.

Apply the value of h=10in V=蟺谤2has follows.

V=蟺谤2hV=蟺谤210V=10蟺谤2

The equation that relates the volumeV and radiusr of the cylinder isV=10蟺谤2.

04

Step 4. Apply the differentiation.

Apply the differentiation to V=10蟺谤2 with respect to t as follows.

ddtV=ddt10蟺谤2dVdt=20蟺谤drdt

The derivativedVdtanddrdtare related by.

05

Step 5. Conclusion.

The equation that relates the volume V and the radius r of the cylinder is V=10蟺谤2.

The derivativedVdtanddrdtare related bydVdt=20蟺谤drdt.

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