Calculating the Total Surface Area of a Cube: A Comprehensive Guide

Understanding the total surface area of a three-dimensional object such as a cube is crucial for various applications, from academic studies to real-world scenarios. This guide will walk you through the process of calculating the total surface area of a cube with a side length of 600 cm, and it will also cover the conversion from square centimeters (cm2) to square meters (m2).

What is the Formula for the Surface Area of a Cube?

Before delving into the calculations, it is essential to understand the formula for determining the total surface area of a cube. The formula is as follows:

Total Surface Area of a Cube 6a2

Step-by-Step Calculation

Given the side length 'a' of the cube is 600 cm, we can calculate the total surface area step by step.

Step 1: Determine the Area of One Face

Each face of a cube is a square, and the area of a square is given by:

A a2

Substituting the given side length:

A (600 cm)2 360000 cm2

Step 2: Calculate the Total Surface Area

A cube has six identical faces, so the total surface area is:

Total Surface Area 6 × A 6 × 360000 cm2 2160000 cm2

Step 3: Convert the Surface Area from cm2 to m2

Since 1 square meter (m2) is equal to 10000 square centimeters (cm2), we can convert the result as follows:

2160000 cm2 ÷ 10000 216 m2

Therefore, the total surface area of the cube is 216 square meters.

Conclusion

Understanding the total surface area of a cube is valuable for various applications, including construction, packaging, and physics. By using the correct formula and following the step-by-step calculations, you can easily determine the total surface area of a cube with a side length of 600 cm, which is 2160000 cm2 or 216 m2.