Math Example--Area and Perimeter--Circular Area and Circumference: Example 16

Topic

Geometry

Description

This example features two concentric circles with radii of 5 and 4 units, and a shaded sector with a central angle of 30 degrees. The task is to calculate the area of the shaded region. The solution involves using the central angle to determine the fractional area difference between the larger and smaller circles: Area = (θ / 360) * (π * r₁² - π * r₂²) = (30 / 360) * (π * 5² - π * 4²) = π / 12 * (25 - 16) = 3π / 4.

Understanding area calculations for sectors of concentric circles helps students develop a more comprehensive grasp of circular geometry. This example builds upon previous concepts while introducing the idea of subtracting areas to find regions between circles.

Presenting multiple examples that explore different aspects of circular geometry helps students develop a deeper 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 why we subtract the areas of the two circles. How does this relate to the concept of area? Can you visualize how the shaded region would change if we altered the central angle or the radii of the circles?"

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