Space Diagonal of Obtuse Edged Cuboid given Cuboidal Height Calculator

Formula Used:

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

Inner Length of Obtuse Edged Cuboid:

Inner 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 in this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( l_{Inner} \) — Inner Length of Obtuse Edged Cuboid (m)
\( w_{Inner} \) — Inner 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 calculates the space diagonal by considering both the inner dimensions of the cuboid and the effect of the cut width on the overall geometry.

3. Importance of Space Diagonal Calculation

Details: Calculating the space diagonal is important in geometry and engineering applications where understanding the maximum distance between opposite vertices is crucial for structural analysis, packaging design, and spatial optimization.

4. Using the Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers greater than zero. The calculator will compute the space diagonal using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is an Obtuse Edged Cuboid?
A: An Obtuse Edged Cuboid is a three-dimensional geometric shape formed by regularly cutting off edges from a standard cuboid, resulting in faces that meet at obtuse angles.

Q2: Why is the cut width important in this calculation?
A: The cut width determines how much material is removed from the original cuboid's edges, which affects both the inner dimensions and the overall geometry of the resulting shape.

Q3: Can this formula be used for any cuboid?
A: This specific formula is designed for obtuse edged cuboids where edges have been regularly cut. For standard cuboids, a simpler formula (√(l²+w²+h²)) would apply.

Q4: What are practical applications of this calculation?
A: This calculation is useful in manufacturing, architecture, and packaging design where objects with chamfered or rounded edges are common.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when accurate measurements are provided. The result is rounded to six decimal places for practical use.