Inner Width of Obtuse Edged Cuboid given Space Diagonal Calculator

Formula Used:

\[ wInner = \sqrt{(dSpace - 2 \times \sqrt{\frac{wCut^2}{6}})^2 - hInner^2 - lInner^2} \]

Space Diagonal of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Inner Height of Obtuse Edged Cuboid:

Inner Length of Obtuse Edged Cuboid:

Inner Width of Obtuse Edged Cuboid:

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1. What is Inner Width of Obtuse Edged Cuboid?

The Inner Width of Obtuse Edged Cuboid is the width of the smaller cuboid formed after edges are regularly cut off from the original cuboid to form the Obtuse Edged Cuboid. It represents the distance between the inner parallel faces of the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ wInner = \sqrt{(dSpace - 2 \times \sqrt{\frac{wCut^2}{6}})^2 - hInner^2 - lInner^2} \]

Where:

\( wInner \) — Inner Width of Obtuse Edged Cuboid (m)
\( dSpace \) — Space Diagonal of Obtuse Edged Cuboid (m)
\( wCut \) — Cut Width of Obtuse Edged Cuboid (m)
\( hInner \) — Inner Height of Obtuse Edged Cuboid (m)
\( lInner \) — Inner Length of Obtuse Edged Cuboid (m)

Explanation: This formula calculates the inner width by considering the space diagonal, cut width, inner height, and inner length of the obtuse edged cuboid.

3. Importance of Inner Width Calculation

Details: Calculating the inner width is crucial for understanding the internal dimensions of obtuse edged cuboids, which is important in various engineering and architectural applications where precise measurements are required.

4. Using the Calculator

Tips: Enter all values in meters. Space Diagonal, Cut Width, Inner Height, and Inner Length must be positive values greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an Obtuse Edged Cuboid?
A: An Obtuse Edged Cuboid is a three-dimensional shape formed by regularly cutting off edges from a original cuboid, resulting in a shape with obtuse angles at the edges.

Q2: Why is the square root function used in this formula?
A: The square root function is used to calculate distances and dimensions based on the Pythagorean theorem, which is fundamental in spatial geometry calculations.

Q3: What are typical applications of this calculation?
A: This calculation is commonly used in manufacturing, architecture, and 3D modeling where precise internal dimensions of modified cuboid shapes need to be determined.

Q4: Can this formula be used for other polyhedral shapes?
A: This specific formula is designed for obtuse edged cuboids. Other polyhedral shapes may require different formulas based on their geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when accurate input values are provided. The result's practical accuracy depends on the precision of the input measurements.