1. if? point} Make sure you start with a rectangular sheet of cardboard or paper. A rectangle has a width and a length that are not the same. Do not use a square piece of card ooard. Stiff paper. cereal fronts or backs are good sources of materials. With. a n.Iler measure the length and width. Write your result here. 2. {It points} Next. make a square pattern that you can use to cut out the blue four corners as shown in this diagram. The square pattern is denoted in the picture by the blue square. You can make a template to use for the pattern from a post note or from an ind ex card which you cut to malre a square. A square must have equal side lengths. A template is something you can use to trace onto your rectangular sheet. All squares cutout should be the same exact size. He precise and neat. It can affect your measurements. Write down the length of a side of the square you chose here Square pattern Mark on cardboard then cut out the corners Fold up on dotted line and tape together to form your open top box. 3. (7 points) Take a picture of your box to eventually upload as part of your assignment. You can insert it in your document. Answer the following questions about your box. 4. (7 points) Measure the longest part of the box and give that answer here. 5. (7 points) Measure the width of the box and give that answer here. 6. (7 points) Measure the height of the box and give that answer here. 7. (7 points) What was the measure of the length of a side of your square pattern template? (You measured this in #2) #5 and #6 should match 8. (7 points) What is the Volume of the box. Show how you got your answer. Write out the formula and show work. So far, the size of the cardboard rectangle was arbitrary depending on what you had to work with. The size of the square you chose. Imagine all the possible looking boxes that could be created. However,9. (7 points) There is a square pattern of size x that will produce a box that will have a maximum volume when you are given a rectangular sheet of material. A graph can show us what value that will be and also will show us what that maximum volume is. The desmos graphing calculator does exactly that. Note: The desmos graphing calculator is free to download onto your computer and it is extremely accurate in finding the values you will be asked for. Using the formula V=x (L-2x)(W-2x) where L is the length of the original rectangle you began with and W is the width of that same rectangle, substitute your numbers for L and W and graph the expression in a Desmos Graphing Calculator at https://www.desmos.com/calculator (you will have to do this on a computer) and determine the value of x that would have produced the maximum volume of your box. You will need to scroll to the top of the graph to find the turning point of the graph and place your mouse at the top and it will show , as an ordered pair, the (x value, max volume). Write the value of x here. 10. (7 points) Copy the graph using Snipping Tool or PrtSon (Print Screen-a key on your keyboard F8 possibly) and paste into this document. The graph should show the ordered pair you found in #8. 11. (7 points) Comparing your box with The Maximum Volume Box In # 8 you calculated the volume of your box. Write the answer again here. Write the size of the length of a side of the square template you used from #2 here: In # 9 you found the value of the length of the square template that would produce the maximum volume. Write the maximum volume from #9 here. Is the maximum volume from #9 greater than the volume of your box? Yes or No Circle one. Think Critically: If the box from the graph shows the size of the square to be cut for maximum volume, then shouldn't the maximum volume given by the graph be greater than the volume of your box