Math Example--Area and Perimeter--Surface Area: Example 12

Topic

Surface Area

Description

This example presents a general formula for calculating the surface area of a hollow cylinder with an outer radius y, an inner radius y - 1, and a height x. The surface area is determined by subtracting the hollow region's area from the full cylinder's surface area. The formula used is SA = 2πr₁² - 2πr₂² + 2πr₁h, which simplifies to SA = 2π(2y + xy - 1), where r₁ is the outer radius (y) and r₂ is the inner radius (y - 1).

Understanding surface area calculations for hollow three-dimensional shapes with variable dimensions is crucial in advanced mathematics and its applications. This collection of examples helps teach the topic by presenting progressively challenging scenarios, allowing students to apply and extend their knowledge of basic surface area principles to more sophisticated problems with general formulas for hollow objects.

Engaging with multiple worked-out examples is essential for students to fully comprehend advanced surface area calculations with variables, especially for hollow shapes. Each example builds upon previous concepts while introducing new complexities, helping students develop critical thinking skills and the ability to approach novel geometric problems with confidence and flexibility, particularly when dealing with hollow objects and variable dimensions.

Teacher's Script: In this example, we're exploring a generalized formula for the surface area of a hollow cylinder. Notice how we use variables to represent dimensions, making our formula applicable to various sizes of hollow cylinders. As we work through this, think about how this general approach relates to the specific hollow cylinder example we saw earlier. This type of thinking will be invaluable as you encounter more complex geometric problems involving hollow objects in your future studies and real-world applications.

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