You have 360cm of wire to make the edges of a prism. Your prism can have any base shape you like, and any height, as long as the total length of all edges is no greater than 360cm.
Your task is to investigate and find answers to the following two questions:
What is the largest possible volume of a prism that can be made in this way?
What is the largest possible surface area of a prism that can be made in this way?
Your submission must include the following:
1. A completed plan sheet (attached), describing the process you intend to use to investigate the problem.
2. A detailed description of your solution to the problem (minimum 2 A4 pages). This should include:
• A description of what you actually did to investigate the problem. Explain the steps you followed and why, and describe any difficulties you encountered and how you tried to resolve them. You may use diagrams and/or graphs to support your explanations.
• Example calculations for the surface area and volumes of at least 2 prisms with different base shapes, and with total edge length at most 360cm.
• Precise descriptions of the prism(s) that you believe have the largest possible volume and surface area.
• A detailed justification of why you believe your chosen prism(s) have the largest possible volume and surface area.
3. A completed reflection sheet (attached).
Submission and Assessment:
You may submit your investigation either as a hard copy to your maths teacher, or as an electronic copy (in which case you may complete the Plan and Reflection in Word and upload this document). Your teacher may instruct you regarding their preferred method of submission.
Your investigation will be given a mark out of 20 according to the rubric on the following page.
Learning Objectives:
1. Consolidate understanding of surface area and volume calculations for 3D prisms, and explore relationships between these measurements and properties of the prisms.
2. Develop skills in independently planning, implementing and reflecting upon an investigative process to solve a mathematical problem.
Important:
The report you submit must be your own work. This means that (although you may discuss the problem with others) you must write your report independently to demonstrate your individual understanding.
Plan (complete this BEFORE you start investigating the problem)
In the box below, describe what you intend to do to investigate the problem. The following questions might help:
How will you begin? What steps should you follow, and in what sequence? What difficulties might you encounter and how will you deal with them? What equipment will you need? How will you know if your answers are correct? How will you communicate your processes and reasoning to others?
