Modeling Box Volume with Polynomials

In this video, Mr. Back explains how to model with polynomial functions by designing a cardboard box with a specific volume. Starting with a sheet of cardboard, the task is to cut out squares from each corner to form a box with a volume of 484 cubic inches. The video covers calculating the volume of a rectangular prism, using a volume formula, and graphing the equation to find the appropriate cut-out size. The process involves using a calculator to graph the volume equation and find intersection points that indicate the correct dimensions for the cut-outs. The video concludes with a summary of the findings.

What is the primary goal of the video tutorial?

• To calculate the area of a rectangle.

• To understand how to model with polynomial functions.

• To learn how to construct a cardboard box.

• To design a new type of cardboard material.

What is the initial size of the cardboard sheet used for the box?

• 30 inches wide and 15 inches long

• 25 inches wide and 20 inches long

• 20 inches wide and 25 inches long

• 15 inches wide and 30 inches long

How is the height of the box determined?

• By the length of the cardboard

• By the width of the cardboard

• By the size of the square cut from each corner

• By the volume of the box

What is the formula used to calculate the volume of the box?

• Length + Width + Height

• Length x Width x Height

• Width x Height

• Length x Width

Why is the Y max adjusted to 1000 in the graphing calculator?

• To change the X-axis scale

• To zoom in on the graph

• To make the graph taller

• To make the graph wider

What range of X values is considered for the box design?

• 5 to 15

• 0 to 5

• 0 to 10

• 10 to 20

What feature of the calculator is used to find the intersection points?

• Zoom feature

• Intersection feature

• Trace feature

• Graph feature

What is the first x value found that satisfies the volume requirement?

• 3.56 inches

• 4.78 inches

• 2.34 inches

• 1.22 inches

What is the second x value found that satisfies the volume requirement?

• 7.89 inches

• 6.87 inches

• 5.67 inches

• 8.90 inches

What is the desired volume of the box?

• 584 cubic inches

• 484 cubic inches

• 684 cubic inches

• 384 cubic inches