# The function that models volume of a cylinder in terms of its radius whose height is four times its radius. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 4P
To determine

## To find: The function that models volume of a cylinder in terms of its radius whose height is four times its radius.

Expert Solution

The function is modeled as V(w)=4πr3 .

### Explanation of Solution

Volume (V) of a cylinder is,

V=Areaofcicularbase×height

The radius of cylinder is r and h is height of cylinder.

Model the function in single variable r .

The height (h) is four times its radius, express it algebraically.

h=4r

Area of circular base is,

Area=πr2

Summarize all the information in a table as shown below,

 In Words In Algebra Radius of cylinder r Height of cylinder 4r Area of Circular base πr2

Model an equation form the above information.

V=Areaofcicularbase×heightV(w)=πr2(4r)=4πr3

Thus, the function is modeled as V(w)=4πr3 .

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