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 2, Problem 11P
To determine

To find: The function that model surface area of rectangular box in terms of length x of one side of its square base whose volume is 60ft3 .

Expert Solution

Answer to Problem 11P

The function that model surface area in terms of the length is 240x+2x2 .

Explanation of Solution

Surface area (S) of rectangular box is,

S=Areaoffoursides+Areaoftopandbottom

Volume of a rectangular box is,

V=(basearea)(height)=Ah

Length of the side of its base is x and base is a square.

Area of square is,

A=(Side)(Side)=xx=x2

Calculate h in terms of x .

V=Ah

Substitute 60 for V in above equation and solve for h .

60=x2h60x2=h

Area of four sides is,

Areaoffoursides=4x(60x2)=240x

Area of top and bottom faces of rectangular box is,

Areaoftopandbottomfaces=2x2

Summarize all the information in a table as shown below.

In Words In Algebra
Area of square base x2
Height 60x2
Area of four sides 240x
Area of top and bottom faces 2x2

Use the information in the table and model the function.

S=Areaoffoursides+Areaoftopandbottomfaces=240x+2x2

Thus, the function that model surface area in terms of the length is 240x+2x2 .

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