Length of Cut Cuboid given Volume Calculator

Formula Used:

\[ Length\ of\ Cut\ Cuboid = \frac{Volume\ of\ Cut\ Cuboid + \frac{Missing\ Length \times Missing\ Height \times Missing\ Width}{6}}{Height \times Width} \]

Volume of Cut Cuboid:

m³

Missing Length of Cut Cuboid:

Missing Height of Cut Cuboid:

Missing Width of Cut Cuboid:

Height of Cut Cuboid:

Width of Cut Cuboid:

Length of Cut Cuboid:

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1. What is the Length of Cut Cuboid Formula?

The Length of Cut Cuboid formula calculates the length dimension of a cuboid with a cut portion, given its volume and other dimensional parameters. It accounts for the missing portion of the cuboid in the calculation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Length\ of\ Cut\ Cuboid = \frac{Volume\ of\ Cut\ Cuboid + \frac{Missing\ Length \times Missing\ Height \times Missing\ Width}{6}}{Height \times Width} \]

Where:

Volume of Cut Cuboid — Total volume of the cut cuboid (m³)
Missing Length — Length of the missing cut portion (m)
Missing Height — Height of the missing cut portion (m)
Missing Width — Width of the missing cut portion (m)
Height — Height of the remaining cuboid (m)
Width — Width of the remaining cuboid (m)

Explanation: The formula reconstructs the original length by accounting for both the remaining volume and the volume of the missing cut portion.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for geometric modeling, architectural design, material estimation, and engineering applications involving cut or modified cuboid shapes.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a cut cuboid?
A: A cut cuboid is a rectangular prism that has had a portion removed, typically by a planar cut, resulting in a more complex geometric shape.

Q2: Why is there a division by 6 in the formula?
A: The division by 6 accounts for the volumetric proportion of the missing cut portion, which is typically a triangular prism or related shape.

Q3: Can this formula be used for any type of cut?
A: This specific formula is designed for cuts that result in the missing portion being proportional to the dimensions provided. Different cut types may require different formulas.

Q4: What if my missing dimensions are zero?
A: If all missing dimensions are zero, the formula simplifies to calculating the length of a complete cuboid from its volume, height, and width.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the assumed geometric model. Accuracy in practical applications depends on precise measurement of input parameters.