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 87E
To determine

To find: The height of storage bin.

Expert Solution

Answer to Problem 87E

The height of storage bin is 18 ft.

Explanation of Solution

Given:

A storage bin made from a cylindrical section surmounted by a conical tin roof. Height of roof is one-third of the storage bin.

The total volume of structure is 1400πft3 and radius is 10ft .

Formula used: Volume of cone and volume of cylinder

Volumeofcone=13πr2h and Volumeofcylinder=πr2h

Calculation:

Let the height of storage bin be h.

Tabulate the given information into the language of algebra.

In words In algebra
Height of storage bin h
Height of conical tin roof 13h
Height of cylindrical section h13h=23h

Model the equation for the above information.

(Volumeofcylindricalsection)+(Volumeofconicalroof)=Totalvolumeπ(10)2(23h)+13π(10)2(13h)=1400π

Simplify the above equation.

2003πh+1009πh=1400π600πh+100πh9=1400π(MultiplybyLCD9)700πh9=1400π700πh=12600π

Further simplify the above equation.

h=12600π700πh=18

Thus, the height of storage bin is 18 ft.

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