Volume of Cut Cuboid given Width to Height Slant Line Calculator

Volume of Cut Cuboid Formula:

\[ V = (l \times h \times w) - \frac{l_{Missing} \times \sqrt{l_{Slant(WH)}^2 - w_{Missing}^2} \times w_{Missing}}{6} \]

Length of Cut Cuboid:

Height of Cut Cuboid:

Width of Cut Cuboid:

Missing Length of Cut Cuboid:

WH Slant Line of Cut Cuboid:

Missing Width of Cut Cuboid:

Volume of Cut Cuboid:

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1. What is Volume of Cut Cuboid?

The Volume of Cut Cuboid is the total quantity of three dimensional space enclosed by the surface of a Cut Cuboid. It represents the space occupied by a cuboid with a portion cut off from one of its corners.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = (l \times h \times w) - \frac{l_{Missing} \times \sqrt{l_{Slant(WH)}^2 - w_{Missing}^2} \times w_{Missing}}{6} \]

Where:

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

Explanation: The formula calculates the volume by subtracting the volume of the cut-off triangular prism from the volume of the complete cuboid.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining material requirements, structural analysis, and spatial planning in construction and manufacturing applications involving cut cuboids.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive and valid. The WH Slant Line must be greater than the Missing Width to maintain mathematical validity.

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 from a regular cuboid, creating a slanted face.

Q2: What units should I use for input?
A: All inputs should be in meters (m) for consistent volume calculation in cubic meters (m³).

Q3: Can the Missing Length or Missing Width be zero?
A: Yes, if either is zero, it means there's no cut in that dimension, and the shape becomes a simpler form.

Q4: What if the WH Slant Line is smaller than the Missing Width?
A: This would result in an imaginary square root, indicating invalid input dimensions. The WH Slant Line must always be greater than the Missing Width.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input dimensions, assuming perfect geometric shapes.