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Chapter 3: Q. 24 (page 299)

In Exercises 19–26, 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 height h of a cone with a fixed radius of 3 units.

Short Answer

Expert verified

Equation relating the quantities:V=3πh

Implicit differentiation:dVdt=3πdhdt

Step by step solution

01

Step 1. Given information 

Volume of the cone=V

Radius of the cone =3

Height of the cone =h

02

Step 2. Equation relating the quantities 

Volume of the cone is given by,

V=πr2h3⇒V=π(32)h3⇒V=3πh

03

Step 3. Implicit differentiation with respect to time

From the above step,

V=3πhDifferentiatingonbothsides,weget,dVdt=3πdhdt

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