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

Formula Used:

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

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 Height of Obtuse Edged Cuboid:

Volume of Obtuse Edged Cuboid:

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1. What is Volume of Obtuse Edged Cuboid?

The Volume of Obtuse Edged Cuboid is the amount of three dimensional space occupied by an Obtuse Edged Cuboid, which is formed by regularly cutting off edges from an original cuboid, creating a polyhedron with obtuse edges.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( V \) — Volume of Obtuse Edged Cuboid (m³)
\( l_{Inner} \) — 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)
\( h_{Cuboid} \) — Cuboidal Height of Obtuse Edged Cuboid (m)

Explanation: The formula accounts for the volume of the inner cuboid plus the volumes of the cut-off edge sections and corner pieces.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining material requirements, structural analysis, and geometric modeling of complex polyhedral shapes with obtuse edges.

4. Using the Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers representing valid geometric measurements.

5. Frequently Asked Questions (FAQ)

Q1: What is an Obtuse Edged Cuboid?
A: An Obtuse Edged Cuboid is a polyhedron formed by cutting off the edges of a regular cuboid, resulting in faces that meet at obtuse angles.

Q2: How is this different from a regular cuboid volume?
A: The formula accounts for the additional volume from the cut-off edge sections and corner pieces that are not part of the inner cuboid.

Q3: What units should I use for the inputs?
A: All inputs should be in consistent units (meters recommended), and the output volume will be in cubic units of the input.

Q4: Are there any limitations to this formula?
A: This formula assumes regular, symmetric cutting of edges and may not apply to irregular or non-uniform edge cutting patterns.

Q5: Can this be used for engineering applications?
A: Yes, this formula is useful for calculating material volumes in manufacturing, construction, and 3D modeling applications involving obtuse-edged cuboids.