BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1.6, Problem 85E
To determine

To find: The height of pile.

Expert Solution

Answer to Problem 85E

The height of pile is 7.52 ft.

Explanation of Solution

Given:

The diameter of conical pile is three time the height of pile.

The volume of pile is 1000ft3 .

Calculation:

Let the height of pile be x.

Tabulate the given information into the language of algebra.

In words In algebra
Height of pile x
Diameter of pile 3x
Radius of pile 3x2

Model the equation for the above information.

Volumeofconicalpile=13π(radius)2×height1000=13π(3x2)2×x

Simplify the above equation for x.

13×227×9x24×x=1000198x384=1000x3=424.24x=7.52

Thus, the height of pile is 7.52 ft.

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