Math Example--Area and Perimeter--Surface Area: Example 11

Topic

Surface Area

Description

This example demonstrates the calculation of surface area for a hollow cylinder with an outer radius of 10 units, an inner radius of 9 units, and a height of 15 units. The surface area is determined by subtracting the area of the hollow region from the full cylinder's surface area. The formula used is SA = 2πr₁² - 2πr₂² + 2πr1h, where r₁ is the outer radius and r₂ is the inner radius. For this specific hollow cylinder, the calculation yields a surface area of 338π square units.

Understanding surface area calculations for hollow three-dimensional shapes 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 involving hollow objects.

Exposure to multiple worked-out examples is vital for students to fully comprehend advanced surface area calculations, 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, particularly when dealing with hollow objects and their unique characteristics.

Teacher's Script: In this example, we're exploring the surface area of a hollow cylinder. Notice how we adapt our previous knowledge of solid cylinders to account for the hollow interior. We'll calculate the surface area of the full cylinder, then subtract the area of the hollow region. This approach will be useful when you encounter similar problems in real-world applications, such as in engineering or manufacturing where hollow cylinders are common.

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