You are required to make an electronic presentation (Microsoft PowerPoint or equivalent) of between 5 and 10
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Question:
You are required to make an electronic presentation (Microsoft PowerPoint or equivalent) of between 5 and 10 minutes duration, to include calculations, graphs, diagrams and pictures of a physical (e.g. cardboard or similar) model, as designed below. Each slide should have an audio commentary with it. Mathematical elements should demonstrate use of an equation editor, and be formatted appropriately. The presentation must be uploaded to Turnitin.
The problem:
- A company marketing sports goods wishes to make a new display container for their colored table tennis balls.
- The current display case is a simple cubic box of volume 0.01 m3 with no top.
- The new model must have the same volume, have no top, but have a regular octagon base.
- To minimize costs the boxes must be made with the minimum surface area. Each of the sides of the base will be x in length.
- You must calculate and demonstrate the value of the side lengths x, and the height of the box, in order to satisfy these constraints.
- You will need to derive an expression for the surface area S using a net and plot a graph of S against x to identify the minimum value of x visually. You then need to use calculus to identify and verify the value of x exactly.
You will then need to estimate how many table-tennis balls of the standard ITTF diameter (40mm) the design will hold, without protruding, supported by mathematical evidence.
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