Math Example--Area and Perimeter--Circular Area and Circumference: Example 12

Topic

Geometry

Description

This example features a circle with a radius of 5 units and a shaded sector with central angle θ (theta). The task is to express the area of the shaded sector in terms of θ. The solution involves using the central angle to find the fractional amount of the total area: Area = (θ / 360) * (π * 5²) = 25π / 360 * θ = 5π / 72 * θ.

Calculating sector areas with variable angles helps students understand the relationship between central angles and portions of a circle's area. This example builds upon previous concepts while introducing the idea of expressing solutions in terms of a variable angle.

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: "Consider how this calculation relates to finding the full area of the circle. How does the expression 5π / 72 * θ represent the portion of the circle we're interested in? Can you predict how the area would change if we doubled the central angle?"

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