Edge Length of Truncated Cube given Volume Calculator

Formula Used:

\[ Edge\ Length\ of\ Truncated\ Cube = \left(\frac{3 \times Volume\ of\ Truncated\ Cube}{21 + (14 \times \sqrt{2})}\right)^{1/3} \]

Edge Length of Truncated Cube:

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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 the truncated cube, which is an Archimedean solid obtained by truncating the vertices of a cube.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Edge\ Length = \left(\frac{3 \times Volume}{21 + (14 \times \sqrt{2})}\right)^{1/3} \]

Where:

\( Volume \) — Volume of the truncated cube (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the edge length of a truncated cube based on its volume, using the mathematical relationship derived from the geometry of the shape.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the dimensions and properties of a truncated cube, which is important in various fields including geometry, architecture, and material science.

4. Using the Calculator

Tips: Enter the volume of the truncated cube in cubic meters. The volume must be a positive value greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cube?
A: A truncated cube is an Archimedean solid that results from truncating the vertices of a cube, creating a polyhedron with 14 faces (8 regular triangles and 6 regular octagons).

Q2: Why is the formula structured this way?
A: The formula is derived from the geometric properties of the truncated cube, specifically relating its volume to its edge length through mathematical derivation.

Q3: What units should I use for volume?
A: The calculator uses cubic meters (m³) for volume, but you can use any consistent unit as long as the edge length will be in the corresponding linear unit.

Q4: Can this calculator handle very large or very small volumes?
A: Yes, the calculator can handle a wide range of volume values, as long as they are positive numbers.

Q5: Is the result always accurate?
A: The result is mathematically accurate based on the input volume and the formula, though practical accuracy may depend on the precision of the input value.