Inner Length of Obtuse Edged Cuboid Calculator

Formula Used:

\[ l_{Inner} = l_{Cuboid} - (\sqrt{2} \times w_{Cut}) \]

Inner Length of Obtuse Edged Cuboid:

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1. What is the Inner Length of Obtuse Edged Cuboid?

The Inner Length of Obtuse Edged Cuboid is the length of the smaller cuboid formed after edges are regularly cut off from the original cuboid to form the Obtuse Edged Cuboid. It represents the internal dimension of the modified geometric shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_{Inner} = l_{Cuboid} - (\sqrt{2} \times w_{Cut}) \]

Where:

\( l_{Inner} \) — Inner Length of Obtuse Edged Cuboid (m)
\( l_{Cuboid} \) — Cuboidal Length of Obtuse Edged Cuboid (m)
\( w_{Cut} \) — Cut Width of Obtuse Edged Cuboid (m)
\( \sqrt{2} \) — Mathematical constant (approximately 1.4142)

Explanation: The formula calculates the inner length by subtracting the product of the square root of 2 and the cut width from the original cuboidal length, accounting for the geometric transformation when edges are cut at 45-degree angles.

3. Importance of Inner Length Calculation

Details: Calculating the inner length is crucial for understanding the dimensional changes in geometric transformations, manufacturing processes, and architectural designs where edges are modified to create obtuse angles.

4. Using the Calculator

Tips: Enter the cuboidal length and cut width in meters. Both values must be positive numbers. The calculator will compute the inner length of the obtuse edged cuboid.

5. Frequently Asked Questions (FAQ)

Q1: What is an Obtuse Edged Cuboid?
A: An Obtuse Edged Cuboid is a geometric shape formed by regularly cutting off the edges of a standard cuboid, creating faces with obtuse angles instead of right angles.

Q2: Why does the formula include √2?
A: The √2 factor accounts for the 45-degree angle cut. When edges are cut at 45 degrees, the relationship between the cut width and the resulting dimensional change involves the Pythagorean theorem, which introduces the √2 factor.

Q3: Can this formula be used for other geometric shapes?
A: This specific formula is designed for cuboids with regularly cut edges. Other shapes may require different formulas based on their geometric properties.

Q4: What are practical applications of this calculation?
A: This calculation is useful in manufacturing, woodworking, metalworking, and architectural design where precise dimensional calculations are needed for modified geometric shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when the input values are accurate and the cutting process follows the assumed 45-degree angle pattern.