Cut Width of Obtuse Edged Cuboid given Space Diagonal Calculator

Formula Used:

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

Space Diagonal of Obtuse Edged Cuboid (d_Space):

Inner Length of Obtuse Edged Cuboid (l_Inner):

Inner Width of Obtuse Edged Cuboid (w_Inner):

Inner Height of Obtuse Edged Cuboid (h_Inner):

Cut Width of Obtuse Edged Cuboid (w_Cut):

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1. What is Cut Width of Obtuse Edged Cuboid?

Cut Width of Obtuse Edged Cuboid is the distance between two newly emerged, parallel edges of Obtuse Edged Cuboid, which emerged after edges are regularly cut off from the original cuboid. It represents the amount of material removed from each edge during the cutting process.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( w_{Cut} \) — Cut Width of Obtuse Edged Cuboid (m)
\( d_{Space} \) — Space Diagonal of Obtuse Edged Cuboid (m)
\( l_{Inner} \) — Inner Length 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 cut width by finding the difference between the space diagonal of the obtuse edged cuboid and the diagonal of the inner cuboid, then scaling it appropriately.

3. Importance of Cut Width Calculation

Details: Calculating the cut width is essential for manufacturing processes involving cuboid shaping, architectural design, and geometric modeling where precise edge cutting is required.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive and the space diagonal is greater than the inner diagonal for valid results.

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 new faces and changing the geometry while maintaining symmetry.

Q2: Why is the square root of 6 used in the formula?
A: The factor √6 comes from the geometric relationship between the cut width and the spatial diagonals in the cuboid structure.

Q3: What are typical applications of this calculation?
A: This calculation is used in manufacturing, woodworking, metalworking, and architectural design where precise edge cutting is required.

Q4: Can this formula be used for any cuboid?
A: The formula specifically applies to obtuse edged cuboids where edges have been uniformly cut off from a regular cuboid.

Q5: What if the calculated cut width is negative?
A: A negative result indicates that the input values are inconsistent (space diagonal is smaller than inner diagonal), which is geometrically impossible for a valid obtuse edged cuboid.