GRADE 12 APPLIED MATH

The Problem
You are given a piece of cardboard that is 6 inches by 4 inches. You would like to cut equal-sized squares out of each of the 4 corners and fold the cardboard in such a way to make an open-top rectangular box.
Part A: Complete the table below:

Length of Square Cut, l (inches)

Length of Box (inches)
Width of Box (inches)

Volume of Box, V (cubic inches)
0.25


0.50


0.90
1.40
1.80




Part B: Questions
Consider the function that is defined to be the volume, V, of the box created from cutting the cardboard corners into squares of length l.
1. What are the possible values of l?
2. What is the dependent and independent variable?
3. Using l and V,find a cubic function of best fit.
4. To maximize the volume of the box, what should be the side length of the corner squares?

1 mark for filling in the length and width column in the table
1 mark for filling in the volume column in the table
1 mark for writing the possible values of l
1 mark for identifying the dependent and independent variables
2 marks for the cubic function of best fit
2 marks for determining the side length of the corner squares that maximizes the volume

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