Math Example--Area and Perimeter--Circular Area and Circumference: Example 6

Topic

Geometry

Description

This example presents two concentric circles with radii of 5 and y units. The objective is to express the area of the shaded region between these circles in terms of y. The solution involves subtracting the area of the smaller circle from the area of the larger circle: A = π * (5)² - π * y² = 25π - πy² = π(25 - y²).

Introducing variables in geometric problems helps students bridge the gap between concrete calculations and abstract mathematical thinking. This example builds upon previous concepts while challenging students to work with both known and unknown values simultaneously.

Exposure to a variety of problem types, including those with variables, is crucial for developing mathematical flexibility. These examples prepare students for more advanced topics in algebra and calculus, where understanding the interplay between constants and variables is essential.

Teacher: "Let's explore how the variable y affects our calculation. How does the final expression π(25 - y²) change as y increases or decreases? Can you determine the maximum possible value for this shaded area?"

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