Edge Length of Truncated Cube given Total Surface Area Calculator

Formula Used:

\[ l_e = \sqrt{\frac{TSA}{2 \times (6 + (6 \times \sqrt{2}) + \sqrt{3})}} \]

Edge Length of Truncated Cube (lₑ):

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1. What is the Edge Length of Truncated Cube?

The edge length of a truncated cube is the length of any edge of this Archimedean solid. A truncated cube is formed by cutting off the corners of a cube, resulting in a polyhedron with 14 faces: 8 regular hexagons and 6 regular octagons.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \sqrt{\frac{TSA}{2 \times (6 + (6 \times \sqrt{2}) + \sqrt{3})}} \]

Where:

\( l_e \) — Edge length of truncated cube (m)
\( TSA \) — Total surface area of truncated cube (m²)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{3} \) — Square root of 3 (approximately 1.7321)

Explanation: This formula derives from the relationship between the total surface area and the edge length of a truncated cube, accounting for the areas of both hexagonal and octagonal faces.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties of truncated cubes, including volume calculation, architectural applications, and mathematical modeling of polyhedral structures.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length.

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 (8 hexagons and 6 octagons).

Q2: What units should I use for the total surface area?
A: The calculator expects the total surface area in square meters (m²), but you can use any consistent unit system as long as the edge length will be in the corresponding linear unit.

Q3: Can this formula be used for other truncated polyhedra?
A: No, this specific formula applies only to truncated cubes. Other truncated polyhedra have different surface area to edge length relationships.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications involving geometric calculations.

Q5: How is this calculation useful in real-world applications?
A: This calculation is valuable in architecture, 3D modeling, crystallography, and any field that involves working with polyhedral structures and their geometric properties.