Space Diagonal Of Obtuse Edged Cuboid Given Cuboidal Edges Calculator

Formula Used:

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

Cuboidal Length of Obtuse Edged Cuboid:

Cuboidal Width of Obtuse Edged Cuboid:

Cuboidal Height of Obtuse Edged Cuboid:

Cut Width 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:

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

Where:

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

Explanation: The formula accounts for the reduction in dimensions due to the cut edges and calculates the diagonal distance through the modified cuboid structure.

3. Importance of Space Diagonal Calculation

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

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive numbers. The calculator will compute the space diagonal based on the provided cuboidal dimensions and cut width.

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 obtuse angles at the corners.

Q2: How does the cut width affect the space diagonal?
A: The cut width reduces the effective dimensions of the cuboid, which in turn affects the calculated space diagonal length.

Q3: Can this calculator be used for regular cuboids?
A: Yes, by setting the cut width to zero, the formula simplifies to the standard space diagonal calculation for a regular cuboid.

Q4: What are practical applications of this calculation?
A: This calculation is useful in manufacturing, architecture, packaging design, and any field dealing with modified cuboid structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values, assuming perfect geometric conditions.