Space Diagonal of Bent Cuboid given Volume Calculator

Formula Used:

\[ d_{Space} = \sqrt{l_{First\ Partial}^2 + l_{Second\ Partial}^2 + \left(\frac{V}{(l_{Total} - w) \times w}\right)^2} \]

First Partial Length of Bent Cuboid:

Second Partial Length of Bent Cuboid:

Volume of Bent Cuboid:

m³

Total Length of Bent Cuboid:

Width of Bent Cuboid:

Space Diagonal of Bent Cuboid:

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1. What is Space Diagonal of Bent Cuboid?

The Space Diagonal of Bent Cuboid is the line segment connecting two vertices that are not on the same face. It represents the longest straight line that can be drawn within the bent cuboid structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Space} = \sqrt{l_{First\ Partial}^2 + l_{Second\ Partial}^2 + \left(\frac{V}{(l_{Total} - w) \times w}\right)^2} \]

Where:

\( d_{Space} \) — Space Diagonal of Bent Cuboid (m)
\( l_{First\ Partial} \) — First Partial Length of Bent Cuboid (m)
\( l_{Second\ Partial} \) — Second Partial Length of Bent Cuboid (m)
\( V \) — Volume of Bent Cuboid (m³)
\( l_{Total} \) — Total Length of Bent Cuboid (m)
\( w \) — Width of Bent Cuboid (m)

Explanation: The formula calculates the space diagonal by considering the geometric properties of the bent cuboid, including its partial lengths, total length, width, and volume.

3. Importance of Space Diagonal Calculation

Details: Calculating the space diagonal is crucial for understanding the maximum internal dimensions of bent cuboid structures, which is important in architectural design, packaging, and spatial analysis.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure that Total Length is greater than Width for valid calculation. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Bent Cuboid?
A: A Bent Cuboid is a three-dimensional shape formed by bending a cuboid at a right angle, creating two perpendicular sections.

Q2: Why is the space diagonal important?
A: The space diagonal helps determine the maximum possible length of objects that can fit inside the bent cuboid structure.

Q3: 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.

Q4: What if Total Length equals Width?
A: The denominator becomes zero, making the calculation invalid. Total Length must be greater than Width.

Q5: How accurate is the calculation?
A: The calculation provides results with up to 6 decimal places precision, suitable for most engineering and architectural applications.