Total Surface Area of Truncated Cube Calculator

Total Surface Area of Truncated Cube Formula:

\[ TSA = 2 \times (6 + (6 \times \sqrt{2}) + \sqrt{3}) \times le^2 \]

Total Surface Area of Truncated Cube:

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1. What is the Total Surface Area of Truncated Cube?

The Total Surface Area of a Truncated Cube refers to the total area of all the faces of the truncated cube. A truncated cube is an Archimedean solid created by truncating the vertices of a cube, resulting in a polyhedron with 14 faces: 6 regular octagons and 8 equilateral triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times (6 + (6 \times \sqrt{2}) + \sqrt{3}) \times le^2 \]

Where:

\( TSA \) — Total Surface Area of Truncated Cube (m²)
\( le \) — Edge Length of Truncated Cube (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{3} \) — Square root of 3 (approximately 1.7321)

Explanation: The formula accounts for the combined surface areas of all the octagonal and triangular faces of the truncated cube.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is important in geometry, architecture, and material science for determining material requirements, heat transfer calculations, and structural analysis of truncated cube-shaped objects.

4. Using the Calculator

Tips: Enter the edge length of the truncated cube in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cube?
A: A truncated cube is an Archimedean solid obtained by cutting off the corners of a regular cube, resulting in a polyhedron with 14 faces (6 octagons and 8 triangles), 36 edges, and 24 vertices.

Q2: How is this formula derived?
A: The formula is derived by calculating the areas of all the octagonal and triangular faces and summing them up, taking into account the geometric relationships between the edge lengths.

Q3: What are the units for the result?
A: The result is in square meters (m²), or whatever square unit corresponds to the input edge length unit.

Q4: Can this calculator handle different units?
A: The calculator uses the same unit for both input and output. If you input centimeters, the result will be in square centimeters.

Q5: What are some real-world applications of truncated cubes?
A: Truncated cube shapes are used in architecture, crystal structures, molecular modeling, and various engineering applications where specific geometric properties are required.