Volume Of Obtuse Edged Cuboid Calculator

Volume Of Obtuse Edged Cuboid Formula:

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

Inner Length Of Obtuse Edged Cuboid:

Inner Width Of Obtuse Edged Cuboid:

Inner Height Of Obtuse Edged Cuboid:

Cut Width Of Obtuse Edged Cuboid:

Volume Of Obtuse Edged Cuboid:

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1. What is Volume Of Obtuse Edged Cuboid?

The Volume Of Obtuse Edged Cuboid represents the total three-dimensional space occupied by a cuboid with its edges regularly cut off, creating obtuse angles. It accounts for both the inner cuboid volume and the additional volume from the cut edges.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( l_{Inner} \) — Inner length of the obtuse edged cuboid (m)
\( w_{Inner} \) — Inner width of the obtuse edged cuboid (m)
\( h_{Inner} \) — Inner height of the obtuse edged cuboid (m)
\( w_{Cut} \) — Cut width of the obtuse edged cuboid (m)
\( \sqrt{2} \) — Mathematical constant approximately equal to 1.414

Explanation: The formula calculates the total volume by summing the inner cuboid volume and the additional volumes from the edge cuts, which include wedge-shaped sections and corner pyramids.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for material estimation, structural design, packaging optimization, and various engineering applications where precise spatial measurements are required.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive numbers. The calculator provides results in cubic meters (m³).

5. Frequently Asked Questions (FAQ)

Q1: What is an obtuse edged cuboid?
A: An obtuse edged cuboid is a geometric shape formed by regularly cutting off the edges of a standard cuboid, creating faces with obtuse angles.

Q2: Why is the formula so complex?
A: The complexity arises from needing to account for multiple geometric components: the inner cuboid, the wedge-shaped edge sections, and the pyramidal corner pieces created by the edge cuts.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurements to meters before input, then convert the result accordingly.

Q4: What are practical applications of this calculation?
A: This calculation is used in manufacturing, architecture, packaging design, and any field where objects with chamfered or rounded edges need precise volume measurements.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the defined geometric shape, assuming perfect measurements and a uniform cut width throughout all edges.