Chapter 1.8, Problem 6WE

To determine

The volume of rectangular box in simplest form in terms of given variable.

Answer to Problem 6WE

  $k^3-3k^2+2k\text{ cubic cm}$

Explanation of Solution

Given:

The length, width and height of rectangular box are consecutive integers.

The largest dimension is k cm.

Calculation:

Let the length of the rectangular box be k cm.

Then, let the width be k − 1 cm and let the height be k − 2 cm.

Volume of rectangle:

  $V=length\times width\times height$

Therefore, the volume of the rectangular box will be:

  $\begin{array}{l}V=k\times \left(k-1\right)\times \left(k-2\right)\\ V=\left(k^2-k\right)\left(k-2\right)\\ V=k^3-2k^2-k^2+2k\\ V=k^3-3k^2+2k\text{ cubic cm}\end{array}$