Space Diagonal of Obtuse Edged Cuboid given Cuboidal Length Calculator

Formula Used:

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

Cuboidal Length of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Inner Width of Obtuse Edged Cuboid:

Inner 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 within the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

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

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)
\( h_{Inner} \) — Inner Height of Obtuse Edged Cuboid (m)

Explanation: The formula calculates the space diagonal by considering the modified dimensions after edges are cut from the original cuboid, accounting for both the inner dimensions and the cut width.

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 optimization, structural engineering, and spatial analysis applications.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive numbers greater than zero. The calculator will compute the space diagonal based on the provided dimensions.

5. Frequently Asked Questions (FAQ)

Q1: What is an Obtuse Edged Cuboid?
A: An Obtuse Edged Cuboid is a cuboid where the edges have been regularly cut off, creating beveled or chamfered edges instead of sharp 90-degree corners.

Q2: How does the cut width affect the space diagonal?
A: The cut width reduces the effective length of the cuboid while adding additional diagonal components, resulting in a complex relationship that the formula accurately captures.

Q3: Can this calculator be used for any unit of measurement?
A: While the calculator uses meters, you can use any consistent unit of measurement as long as all inputs are in the same unit.

Q4: What is the significance of the √2 factor in the formula?
A: The √2 factor accounts for the 45-degree angle created by the edge cutting process, which affects the effective dimensions of the cuboid.

Q5: How accurate is this calculation for practical applications?
A: The calculation is mathematically precise for the given geometric model of an obtuse edged cuboid and provides accurate results for engineering and design purposes.