Math Example--Area and Perimeter--Circular Area and Circumference: Example 20

Topic

Geometry

Description

This example features two concentric circles with radii 5 and y, and a shaded sector with a central angle of 30 degrees. The task is to express the area of the shaded region in terms of y. The solution involves calculating the difference between the areas of the larger and smaller circles, accounting for the central angle: Area = π/12 * (25 - y²).

Understanding area calculations for sectors of concentric circles with one variable radius helps students develop a more nuanced grasp of circular geometry. This example builds upon previous concepts while introducing the idea of expressing solutions in terms of a variable radius.

Presenting multiple examples that explore different aspects of circular geometry helps students develop a comprehensive understanding of these concepts. By working through various problem types, students learn to apply formulas flexibly and interpret results in different contexts.

Teacher: "Let's think about how the variable y affects our calculation. How does the expression π/12 * (25 - y²) change as y increases or decreases? Can you determine the maximum possible value for this shaded area, and what does it mean geometrically?"

For a complete collection of math examples related to Circular Area and Circumference click on this link: Math Examples: Circular Area and Circumference Collection.