Chapter 3.2, Problem 45E

To determine

To calculate: To find if the volume of the solid is a linear or non-linear function

Answer to Problem 45E

Volume of solid represents a non-linear function

Explanation of Solution

Given: Solid is

  

Formula Used:

Linear functions are polynomials with degree of $1$ and have constant slopes. Graph of linear function is a straight line

Non-linear functions are polynomials with degree of more than $1$ and have a slope that varies between points. Graph of non-linear function is a curved line

Calculation:

Solid is given as follows:

  

Volume of cuboid is given as

  $Volume=Length\times Width\times Height$

Substituting the values,

  $\begin{array}{l}V=9\times s\times s\\ V=9s^2\end{array}$

Now, degree of equation is $2$

Since the degree of equation is more than $1$ , thus equation is non-linear

Conclusion:

Hence, Volume of solid represents a non-linear function