Volume Of Obtuse Edged Cuboid Given Inner Width And Cut Width Calculator

Formula Used:

\[ V = (l_{Inner} \times w_{Inner} \times h_{Inner}) + \sqrt{2} \times w_{Cut} \times ((l_{Inner} \times w_{Inner}) + (w_{Inner} \times h_{Inner}) + (h_{Inner} \times l_{Inner})) + \left(\frac{(w_{Cuboid} - w_{Inner})}{\sqrt{2}}\right)^2 \times (l_{Inner} + w_{Inner} + h_{Inner}) + \left(\frac{4}{3\sqrt{2}}\right) \times (w_{Cut})^3 \]

Inner Length of Obtuse Edged Cuboid:

Inner Width of Obtuse Edged Cuboid:

Inner Height of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Cuboidal Width of Obtuse Edged Cuboid:

Volume of Obtuse Edged Cuboid:

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1. What is the Volume of Obtuse Edged Cuboid?

The Volume of Obtuse Edged Cuboid represents the total three-dimensional space occupied by a cuboid with its edges cut off at an angle, creating obtuse edges. This calculation is important in various engineering and architectural applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( l_{Inner} \) — 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)
\( w_{Cut} \) — Cut Width of Obtuse Edged Cuboid (m)
\( w_{Cuboid} \) — Cuboidal Width of Obtuse Edged Cuboid (m)

Explanation: The formula accounts for the volume of the inner cuboid plus the additional volume created by the cut edges, incorporating geometric relationships between the different dimensions.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for material estimation, structural design, and space optimization in construction and manufacturing applications involving obtuse-edged cuboids.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive numbers. The calculator will compute the volume based on the mathematical formula provided.

5. Frequently Asked Questions (FAQ)

Q1: What is an obtuse edged cuboid?
A: An obtuse edged cuboid is a three-dimensional shape formed by cutting the edges of a regular cuboid at an angle, creating faces with obtuse angles.

Q2: How is this different from a regular cuboid volume?
A: The volume calculation is more complex as it accounts for the additional space created by the cut edges, unlike the simple length×width×height formula for regular cuboids.

Q3: What are typical applications of this calculation?
A: This calculation is used in architectural design, packaging optimization, and manufacturing processes where materials are cut at angles.

Q4: Are there limitations to this formula?
A: The formula assumes precise geometric cuts and may need adjustment for irregular cuts or non-uniform edge removal.

Q5: Can this calculator be used for imperial units?
A: The calculator currently works with metric units (meters). For imperial units, convert measurements to meters first or modify the formula accordingly.