Calculating Open Box Volume and Dimensions Algebra Word Problem

Published on July 11, 2026

Word-Problem

Solve for the volume of an open box created from a rectangular cardboard by cutting corners and folding. Determine the domain of the volume function and find dimensions for a specific volume.

Question

Answer

Based on the information provided in the problem, let’s solve it step by step.

Given Data:

Let the width of the original rectangular cardboard be cm.
The length of the cardboard is thrice the width, so length cm.
Squares of side cm are cut from each of the four corners.
The cardboard is then folded to form an open box.

Dimensions of the Open Box:

When the corners are cut and the sides are folded up:

The height () of the box will be the side of the cut square: cm.
The width () of the base will be the original width minus two cut-outs: cm.
The length () of the base will be the original length minus two cut-outs: cm.

i. Find the volume of the open box and determine if the function is a polynomial.

The volume

of a rectangular box is given by

Conclusion: The resultant function

is a polynomial function (specifically a quadratic polynomial) because it is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.