Volume of Cut Cuboid given Length to Height Slant Line Calculator

Formula Used:

\[ V = (l \times h \times w) - \frac{\sqrt{l_{slant(LH)}^2 - h_{missing}^2} \times h_{missing} \times w_{missing}}{6} \]

Length of Cut Cuboid:

Height of Cut Cuboid:

Width of Cut Cuboid:

LH Slant Line of Cut Cuboid:

Missing Height of Cut Cuboid:

Missing Width of Cut Cuboid:

Volume of Cut Cuboid:

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1. What is the 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:

\[ V = (l \times h \times w) - \frac{\sqrt{l_{slant(LH)}^2 - h_{missing}^2} \times h_{missing} \times w_{missing}}{6} \]

Where:

\( l \) — Length of Cut Cuboid (m)
\( h \) — Height of Cut Cuboid (m)
\( w \) — Width of Cut Cuboid (m)
\( l_{slant(LH)} \) — LH Slant Line of Cut Cuboid (m)
\( h_{missing} \) — Missing Height 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 space optimization in various engineering and architectural applications.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive and valid. The slant line measurement must be greater than the missing height for valid calculation.

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, resulting in a shape with both rectangular and triangular faces.

Q2: Why is the square root function used in the formula?
A: The square root function calculates the base length of the triangular cut portion using the Pythagorean theorem applied to the slant line and missing height.

Q3: What are the measurement units used?
A: All measurements should be in consistent units (typically meters), and the resulting volume will be in cubic meters (m³).

Q4: What if the slant line is shorter than the missing height?
A: This would result in a negative value under the square root, which is mathematically impossible. Ensure the slant line is always longer than the missing height.

Q5: Can this calculator handle different units?
A: The calculator assumes all inputs are in meters. For other units, convert all measurements to meters first before calculation.