Math Example--Area and Perimeter--Surface Area: Example 21

Topic

Surface Area

Description

This example demonstrates the calculation of surface area for a hollow cube with an outer side length of 9 units and an inner hollow square side length of 7 units. The surface area is calculated using the formula SA = 6 * s₁² - 2 * s₂², where s1 is the outer side length and s2 is the inner side length. For this specific hollow cube, the calculation yields a surface area of 388 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 cube. Notice how we adapt our previous knowledge of solid cubes to account for the hollow interior. We'll calculate the surface area of the full cube, then subtract the area of the two open faces. This approach will be useful when you encounter similar problems in real-world applications, such as in engineering or manufacturing where hollow structures are common.

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