Width of Cut Cuboid given Volume Calculator

Formula Used:

\[ w = \frac{V + \frac{l_{Missing} \times h_{Missing} \times w_{Missing}}{6}}{h \times l} \]

Volume of Cut Cuboid:

m³

Missing Length of Cut Cuboid:

Missing Height of Cut Cuboid:

Missing Width of Cut Cuboid:

Height of Cut Cuboid:

Length of Cut Cuboid:

Width of Cut Cuboid:

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1. What is the Width of Cut Cuboid Formula?

The formula calculates the width of a cut cuboid given its volume, missing dimensions, height, and length. It accounts for the volume of the missing portion to determine the complete width dimension.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ w = \frac{V + \frac{l_{Missing} \times h_{Missing} \times w_{Missing}}{6}}{h \times l} \]

Where:

\( w \) — Width of Cut Cuboid (m)
\( V \) — Volume of Cut Cuboid (m³)
\( l_{Missing} \) — Missing Length of Cut Cuboid (m)
\( h_{Missing} \) — Missing Height of Cut Cuboid (m)
\( w_{Missing} \) — Missing Width of Cut Cuboid (m)
\( h \) — Height of Cut Cuboid (m)
\( l \) — Length of Cut Cuboid (m)

Explanation: The formula reconstructs the complete width by accounting for both the existing volume and the volume of the missing portion.

3. Importance of Width Calculation

Details: Accurate width calculation is crucial for geometric reconstruction, volume verification, and dimensional analysis of cut cuboid shapes in various engineering and architectural applications.

4. Using the Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers. Ensure that height and length are not zero to avoid division by zero errors.

5. Frequently Asked Questions (FAQ)

Q1: What is a cut cuboid?
A: A cut cuboid is a three-dimensional shape formed by cutting off a corner or portion from a complete cuboid.

Q2: Why is the missing volume divided by 6 in the formula?
A: The division by 6 accounts for the geometric properties of the missing tetrahedral portion of the cut cuboid.

Q3: Can this formula be used for irregular cuts?
A: This specific formula applies to standard corner cuts. Irregular cuts may require different mathematical approaches.

Q4: What units should be used for input values?
A: All input values should be in consistent units (preferably meters for length dimensions and cubic meters for volume).

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when all input values are accurate and the cut follows the assumed geometric pattern.