IB MYP Math Investigation Task Area perimenter and arc length of the sector

In this task, you will step into the role of an engineer tasked with optimizing the design of a blender blade. The blade can be modeled as a sector of a circle, and your goal is to use mathematical concepts to determine the most efficient blade design based on the arc length, perimeter, and area of the sector.

Key Concept:

Relationship: Explores the interconnection between variables, objects, or concepts. In this context, it looks at how the geometric properties of sectors (arc length, perimeter, and area) relate to real-world design applications like blender blade efficiency.

Related Concepts:

Approximation: Involves estimating values or simplifying complex models to make calculations more manageable. In this task, students approximate the real-world performance of blades using geometric models.

Models: Representations of real-world phenomena. The circular sectors in this task are mathematical models representing blender blades, which are used to analyze and optimize their design.
Global Context:

Globalization and Sustainability: Focuses on how interconnected systems, like the global economy or environmental sustainability, impact design and resource use. In this investigation, the design of efficient blender blades can be tied to energy consumption and sustainable production methods, emphasizing the need for efficient, durable, and environmentally conscious designs.

Statement of Inquiry: “Understanding the relationship between mathematical models and real-world approximations allows us to optimize product design, promoting efficiency and sustainability in a globalized economy.”

Including the task specific clarification, answer key .

Recommended for MYP4 &5.