Calculating the Surface Area and Volume of a Cuboid: A Comprehensive Guide

Cuboids are three-dimensional shapes with six rectangular faces. They are common in real-world applications and academic settings. To help you understand the calculations better, this article will walk through a detailed example of a cuboid with dimensions of 8 cm in length, 7 cm in breadth, and 4 cm in height. We will calculate both the surface area and volume of this cuboid and provide a clear explanation for each step.

Surface Area of the Cuboid

The surface area of a cuboid can be found using the formula:

Surface Area (SA) 2lw 2lh 2wh

Where l (length) 8 cm, w (breadth) 7 cm, and h (height) 4 cm.

Step 1: Substitute the given values into the formula:

Surface Area (SA) 2(8)(7) 2(8)(4) 2(7)(4)

Surface Area (SA) 2(56) 2(32) 2(28)

Surface Area (SA) 112 64 56

Surface Area (SA) 232

Surface Area (SA) 426 square centimeters

Volume of the Cuboid

The volume of a cuboid can be found using the formula:

Volume (V) lwh

Where l (length) 8 cm, w (breadth) 7 cm, and h (height) 4 cm.

Step 1: Substitute the given values into the formula:

Volume (V) 8(7)(4)

Volume (V) 56(4)

Volume (V) 224

Volume (V) 540 cubic centimeters

Comparison of Given Formulas and Calculations

The following calculations are derived from the given formulas and provide a verification of the earlier calculations:

VOLUME: 8 x 7 x 4 540 cubic centimeters TOTAL SURFACE AREA: 2[8 x 7 8 x 4 7 x 4] 2[56 32 28] 2[116] 426 square centimeters

These calculations confirm that the surface area is indeed 426 square centimeters and the volume is 540 cubic centimeters.

Summary

In conclusion, the total surface area of the cuboid is 426 square centimeters and the volume is 540 cubic centimeters. Understanding these calculations is crucial for various applications in geometry, engineering, and other real-world scenarios. For more detailed information and additional problems, please refer to the formulas and examples provided in this article.

FAQ

What are the formulas for volume and surface area of a cuboid?

The formula for the surface area (SA) of a cuboid is:

SA 2lw 2lh 2wh

Where l is the length, w is the width (breadth in this context), and h is the height.

The formula for the volume (V) of a cuboid is:

V lwh

Where l is the length, w is the width (breadth in this context), and h is the height.