Let's Beat the French: Create a Game-Changing Drink Bottle for Brisbane 2032!

Question

The Brisbane City Council is looking to showcase Australian creativity and heritage by marketing a new water bottlereo celebrate the upcoming Brisbane 2032 Olympics. They have tasked you ing designing a 1-litre bottle that not only serves its practical purpose but also harporales a logo that represents all Australians and honours our history and Aboriginal heritage. Your ear 9 mathematics class has been enlisted to present a comprehensive repare. some design proposals, which the Council can then use to create a proposal for their manume desto reduce material use and promote sustainability.

Design Brief:
1. Variety in Design:
- You are required to design two different containers.
- The shape of the cartons should be selected from the following groups: prisms, pyramids, cylinders, or cones.
2. Volume and Shape:
- The volume of each package must be 1 litre (1000cm*), but the shapes must differ from the standard cylindrical drink containers.
3. Minimizing Material Use:
- The surface area (amount of material used) of the container should be calculated and kept to a minimum.
4. Cultural Representation:
- Each design must feature a logo that creatively represents all Australians and acknowledges our rich history and Aboriginal heritage.

Submission Requirements:
your proposal to the brisbane city counsil must include the following components:
1. Planning document:
- a detailed planning document outlining your designs.
- A recommendation for which design the council should use, supported by reasons. Consideration should include the amount of material used and practical issues that supermarkets may encounter, such as staking and shelf space.
2. 3-D Sketches:
- clear, 3-dimensional sketches of your proposed designs.
3. Scale Drawings:
- Neat, to-scale drawings of the nets for your cartoons, labelled with dimensions.
4. Calculations:
- detailed calculations demonstrating that the volume of the containers meets the 1-litre requirement.
- Calculations of the surface area for each design, highlighting the martial usage.
5. Logo Design:
- A creative logo that represents all Australians and our history, with a focus on Aboriginal heritage.
6. Model:
- An “actual size” model of your recommended design for a bottle.

PLANNING DOCUMENT
1
Interpret the task.

Write a short description of the task.

List the information provided to help you complete the task?

List other information you may need to find out to complete the task fully.

2
Identify the Mathematics

List the units of measurement you will need to consider.

List any formula that might be useful to complete this task.

3
Analyse information and data sources.

List where or who you plan to get the additional information from.

Answer 1

PLANNING DOCUMENT

1. Interpret the Task

Task Description: The Brisbane City Council has tasked our year 9 mathematics class with designing a new 1-litre drink bottle for the Brisbane 2032 Olympics. The bottle design should be unique, minimizing material use while representing Australian heritage, particularly focusing on Aboriginal culture. We are required to create two different container shapes, calculate their volumes and surface areas, and provide visual and practical proposals for the Council's consideration.

Information Provided:

• The drink bottle must hold a volume of 1 litre (1000 cm³).
• The shapes must differ from standard cylindrical containers.
• The surface area should be minimized.
• Each design must feature a logo reflecting Australian and Aboriginal heritage.

Other Information Needed:

• The appropriate dimensions for the selected shapes to achieve the required volume.
• The surface area formulas for different geometric shapes.
• Information on materials that can be used for sustainable practices.

2. Identify the Mathematics

Units of Measurement:

• Volume: cubic centimeters (cm³)
• Surface Area: square centimeters (cm²)
• Dimensions: centimeters (cm)

Useful Formulas:

• Volume of a rectangular prism: \( V = l \times w \times h \)
• Volume of a pyramid: \( V = \frac{1}{3} \times B \times h \) (where B is the base area)
• Volume of a cone: \( V = \frac{1}{3} \times \pi r^2 h \)
• Volume of a cylinder: \( V = \pi r^2 h \) (although not to be used here)
• Surface area of a rectangular prism: \( SA = 2(lw + lh + wh) \)
• Surface area of a pyramid: \( SA = B + \frac{1}{2} \times P \times l \) (where P is perimeter of the base and l is the slant height)
• Surface area of a cone: \( SA = \pi r (r + l) \) (where l is the slant height)
• Surface area of a spherical object (potential inspiration): \( SA = 4 \pi r^2 \)

3. Analyse Information and Data Sources

Information Sources:

• Mathematics textbooks for volume and surface area formulas.
• Online educational resources such as Khan Academy for geometric calculations.
• Research on Australian Aboriginal culture and symbols to create a meaningful logo.
• Survey materials commonly used in sustainable drink bottle production.

Design Proposals (Basic Overview)

• Design 1: Pyramidal Bottle

  • Shape: Square Pyramid
  • Volume Calculation: Ensure the dimensions satisfy \( V = \frac{1}{3} \times \text{base area} \times h \) to reach 1000 cm³.
  • Logo: Incorporate traditional patterns with the boomerang symbol to signify unity.

• Design 2: Tapered Cone Bottle

  • Shape: Cone
  • Volume Calculation: Utilize the volume formula \( V = \frac{1}{3} \times \pi r^2 h \) for 1000 cm³.
  • Logo: Use Indigenous dots and circles to represent the connection of people and land.

Next Steps

1. Sketches: Create 3-D sketches of both designs.
2. Scale Drawings: Prepare to-scale net drawings and dimensions of the two designs.
3. Volume and Surface Area Calculations: Perform all necessary calculations to confirm 1-litre capacity and minimal surface area.
4. Logo Development: Start brainstorming logo designs that meet the requirements for cultural representation.
5. Model Creation: Select materials for an "actual size" physical model of the recommended design.

Recommendation

Based on the calculations and practical considerations, I will evaluate which design is more efficient in terms of materials and functionality for consumers and suggest that as the primary proposal for the council.

This planning document set the groundwork for a comprehensive proposal aimed at achieving a pivotal representation of both design and sustainability for the Brisbane 2032 Olympics drink container.