# The function that models surface area of a cube in terms of its volume.

### 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 8P
To determine

## To find: The function that models surface area of a cube in terms of its volume.

Expert Solution

The function that models area of given rectangle is 6(V23) .

### Explanation of Solution

Surface area of cube is,

S=6a2 (1)

Where S is surface area of cube and a is side of cube.

Volume of cube is,

V=a3 (2)

Where V is volume of cube and a is side of cube.

Take third root of equation (2)

(V)13=a

Summarize all the information in a table as shown below.

 In Words In Algebra Surface Area 6a2 Side (V)13

Use the information in the table and model the function in single variable a .

S=6a2S=6(V13)2=6V23[(xa)b=xab]

Hence, function that models surface area of cube in terms of volume is s.

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