How to Calculate the Total Surface Area of a Cube with 24 cm Edges

Understanding the formula and calculation methods for the surface area of a cube is essential in various mathematical and practical applications. This article aims to guide you through the process of determining the total surface area of a cube with edges measuring 24 cm. We will explore the steps involved, the formula used, and a detailed example to ensure clarity and accuracy.

The Basic Understanding: What is a Cube?

A cube is a three-dimensional geometric figure with six square faces, twelve edges, and eight vertices. Each face of the cube is a square, and all the edges are of equal length. The surface area of a cube refers to the total area of all its faces combined.

The Formula for Calculating the Total Surface Area of a Cube

The total surface area of a cube can be calculated using a straightforward formula. For a cube with edge length E, the formula is:

TSA cube 6 E2

This formula is derived from the fact that a cube has six identical square faces, and the area of one face is E2. Therefore, the total surface area is six times the area of one face.

Step-by-Step Calculation: Total Surface Area of a Cube with Edges of 24 cm

Let's walk through the step-by-step process to find the total surface area of a cube with edges of 24 cm.

Identify the Edge Length: The length of each edge of the cube is given as 24 cm. This will be our E in the formula. Apply the Formula: Substitute the value of the edge length into the formula for the total surface area of a cube.

TSA cube 6E2

TSA cube 6 × (24 cm)2

TSA cube 6 × 576 cm2

TSA cube 3456 cm2

Double Check: Verify the calculation by recalculating. The area of one face is 24 cm × 24 cm 576 cm2. Multiplying this by 6 gives 576 cm2 × 6 3456 cm2. This confirms the initial calculation.

Understanding the Result: 3456 cm3

It is important to note that the result is 3456 cm2, not cm3. The unit cm3 is used for volume calculations, while cm2 is used for surface area calculations. In this case, the units of the result should be cm2, as we are calculating the area of the faces of the cube.

Conclusion and Key Takeaways

In conclusion, the total surface area of a cube with edges of 24 cm is 3456 cm2. This calculation is straightforward and can be applied to any cube by substituting the known edge length into the formula 6E2. Mastering this concept is crucial for solving more complex geometry problems and understanding three-dimensional shapes.

Related Topics

Calculating the Volume of a Cube Surface Area of Rectangular Prisms Geometry in Real-Life Applications

For further exploration of geometric concepts and their real-world applications, consider delving into the topics mentioned above.