Your task is to find the greatest possible volume for an open box with a square base.
Instructions:
Box #1:
find an open box or construct one and measure its length, width and height
Calculate the volume of box #1 and record it.
Calculate the surface area of the box #1 and record it
Let x represent the length & width since it’s a square base
Let h represent the height
Let S represent the surface Area
Box #2:
Use the same surface area of box #1 to create box #2 with a maximized volume.
- Write an equation for the surface area of the box and use it to solve for h
- Write an equation for the volume of the box using the above information
- Graph the volume function in part b
- Find the derivative of V in part b
- What are the values of X and h that will produce a maximum volume for box #2?
- Calculate the new volume based on part-d for the second box
- Calculate the % change in the volume between the box #1 and box #2
Box #3:
- With the same dimensions of the sheet of paper used to construct the box #1, let X denote the amount to be cut from each corner. Find a Function for the volume and find its maximum. Compare your maximized volume for box #3 with that found for box #2 and explain the difference between the two.
