Maximizing Volume of Open-Top Boxes

The video tutorial explains how to form an open top box from a 12x10 inch cardboard by cutting squares from each corner. It derives the volume function of the box and discusses its domain. The tutorial then uses a graphing calculator to graph the volume function and find the dimensions of the square cut that maximizes the volume. The maximum volume and corresponding dimensions are determined using the calculator's maximum feature.

What is the initial size of the cardboard used to form the open-top box?

• 10 inches by 10 inches

• 14 inches by 8 inches

• 12 inches by 10 inches

• 12 inches by 12 inches

What is the expression for the height of the box after cutting squares from each corner?

• 12 inches

• 10 inches

• 2x inches

• x inches

What is the domain of the volume function for the open-top box?

• (0, 12)

• (0, 10)

• (5, 10)

• (0, 5)

What is the expanded form of the volume function V(x)?

• 4x^3 + 44x^2 - 120x

• 4x^3 - 44x + 120

• 4x^2 - 44x + 120

• 4x^3 - 44x^2 + 120x

Which tool is used to graph the volume function to find the maximum volume?

• Compass

• Protractor

• Ruler

• Graphing calculator

What is the purpose of adjusting the window settings on the graphing calculator?

• To better view the graph and find the maximum point

• To change the color of the graph

• To make the graph appear 3D

• To zoom in on the x-axis only

What feature of the calculator is used to find the maximum volume?

• Sum feature

• Average feature

• Minimum feature

• Maximum feature

What is the approximate side length of the square cut from each corner to maximize the volume?

• 1.8107 inches

• 2.5000 inches

• 3.0000 inches

• 4.0000 inches

What is the approximate maximum volume of the box?

• 120.0000 cubic inches

• 100.0000 cubic inches

• 80.0000 cubic inches

• 96.7706 cubic inches

To how many decimal places are the values rounded in the final result?

• 2 decimal places

• 5 decimal places

• 4 decimal places

• 3 decimal places