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

Formula Used:

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

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1. What Is The Volume Of Obtuse Edged Cuboid?

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

2. How Does The Calculator Work?

The calculator uses the formula:

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

Where:

Explanation: This formula accounts for the volume of the inner cuboid, the volume added by the cut edges, and the volume of the corner pieces.

3. Importance Of Volume Calculation

Details: Accurate volume calculation is crucial for determining material requirements, capacity planning, and structural analysis of obtuse edged cuboid shapes in engineering and design applications.

4. Using The Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers. The calculator will compute the volume based on the provided dimensions.

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, resulting in faces that are not perpendicular to each other.

Q2: Why is the formula so complex?
A: The complexity arises from needing to account for multiple components: the inner cuboid volume, the volume added by the cut edges, and the volume of the corner pieces that are removed and added back in different forms.

Q3: What are typical applications of this calculation?
A: This calculation is useful in manufacturing, architecture, and packaging design where objects with softened or beveled edges are common.

Q4: Are there limitations to this formula?
A: The formula assumes regular, symmetric cutting of all edges. It may not be accurate for irregular cuts or non-uniform edge treatments.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurements to meters before inputting them.

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