Understanding the Surface Area of a Cuboid: Formulas, Calculations, and Applications

A cuboid, also known as a rectangular box, is a three-dimensional figure characterized by its length (l), breadth (b), and height (h). In this article, we will explore the mathematical formulas and methods to calculate the surface area of a cuboid and understand their applications in various fields.

Formulas for the Surface Area of a Cuboid

The surface area of a cuboid is calculated using the formula:

Surface Area (SA) 2 (lb bh hl)

Where:

l length of the cuboid b breadth of the cuboid h height of the cuboid

Calculation Steps

Identify the dimensions of the cuboid: length (l), breadth (b), and height (h). Plug these values into the formula: Surface Area (SA) 2 (lb bh hl). Calculate the product of each pair of dimensions: l*b, b*h, and h*l. Add the three products together. Multiply the sum by 2. The result is the surface area of the cuboid in square units.

Example Calculation

Let's consider a cuboid with the following dimensions: length (l) 22 cm, breadth (b) 12 cm, and height (h) 7.5 cm.

Calculation Details

Step-by-step Calculation:

Calculate the individual products: l * b 22 * 12 264 cm2 b * h 12 * 7.5 90 cm2 h * l 7.5 * 22 165 cm2 Add the products: 264 90 165 519 cm2 Multiply the sum by 2: 2 * 519 1038 cm2

Thus, the surface area of the cuboid is 1038 cm2.

Lateral Surface Area of a Cuboid

The lateral surface area (LSA) of a cuboid is the area of all the sides excluding the bottom and top faces:

Lateral Surface Area (LSA) 2 (lh bh)

Total and Area of a Cuboid

Area of a cube can be denoted as s^2, where s is the side length. For a cuboid, the area of each face is calculated as s1s2 or s1s1d, where s1, s2, and d are the side lengths and corresponding dimensions, respectively.

Conclusion

The surface area of a cuboid is a fundamental concept in geometry and has various applications in fields such as construction, engineering, and design. Understanding the formulas and methods to calculate the surface area is essential for solving practical problems.

References:

BBC Bitesize: Surface Area of Cubes and Cuboids Sciencing: The Formula to Calculate the Surface Area of a Cuboid

Further Reading:

Learn more about the video on “How to find the Surface Area of a Cuboid” for visual learners.