Space Diagonal of Obtuse Edged Cuboid Given Inner Width Calculator

Formula Used:

\[ d_{Space} = \sqrt{(l_{Cuboid} - \sqrt{2} \times w_{Cut})^2 + w_{Inner}^2 + (h_{Cuboid} - \sqrt{2} \times w_{Cut})^2} + 2 \times \sqrt{\frac{w_{Cut}^2}{6}} \]

Cuboidal Length of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Inner Width of Obtuse Edged Cuboid:

Cuboidal Height of Obtuse Edged Cuboid:

Space Diagonal of Obtuse Edged Cuboid:

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1. What is Space Diagonal of Obtuse Edged Cuboid?

The Space Diagonal of Obtuse Edged Cuboid is the length of the straight line that runs through the three-dimensional space connecting any two opposite vertices of the Obtuse Edged Cuboid. It represents the longest distance between two points in the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Space} = \sqrt{(l_{Cuboid} - \sqrt{2} \times w_{Cut})^2 + w_{Inner}^2 + (h_{Cuboid} - \sqrt{2} \times w_{Cut})^2} + 2 \times \sqrt{\frac{w_{Cut}^2}{6}} \]

Where:

\( d_{Space} \) — Space Diagonal of Obtuse Edged Cuboid (m)
\( l_{Cuboid} \) — Cuboidal Length of Obtuse Edged Cuboid (m)
\( w_{Cut} \) — Cut Width of Obtuse Edged Cuboid (m)
\( w_{Inner} \) — Inner Width of Obtuse Edged Cuboid (m)
\( h_{Cuboid} \) — Cuboidal Height of Obtuse Edged Cuboid (m)

Explanation: The formula accounts for the geometric properties of the obtuse edged cuboid, considering the cut width and the resulting inner dimensions.

3. Importance of Space Diagonal Calculation

Details: Calculating the space diagonal is crucial for understanding the maximum internal dimensions of the cuboid, which is important in packaging, storage, and structural design applications.

4. Using the Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers 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 cuboid whose edges have been regularly cut off, creating obtuse angles at the edges.

Q2: Why is the square root of 2 used in the formula?
A: The square root of 2 appears due to the 45-degree angle cuts made on the original cuboid's edges.

Q3: What are typical applications of this calculation?
A: This calculation is used in manufacturing, packaging design, architecture, and any field dealing with modified cuboid shapes.

Q4: How accurate is this formula?
A: The formula is mathematically precise for perfectly cut obtuse edged cuboids with uniform cut widths.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert all measurements to meters before calculation.