Volume Of Cut Cuboid Given Residual Edges Calculator

Formula Used:

\[ V = (l \times h \times w) - \frac{(l - l_{Residual}) \times (h - h_{Residual}) \times (w - w_{Residual})}{6} \]

Length of Cut Cuboid:

Height of Cut Cuboid:

Width of Cut Cuboid:

Residual Length of Cut Cuboid:

Residual Height of Cut Cuboid:

Residual 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 that has been partially cut or removed.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = (l \times h \times w) - \frac{(l - l_{Residual}) \times (h - h_{Residual}) \times (w - w_{Residual})}{6} \]

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)
\( l_{Residual} \) — Residual Length of Cut Cuboid (m)
\( h_{Residual} \) — Residual Height of Cut Cuboid (m)
\( w_{Residual} \) — Residual Width of Cut Cuboid (m)

Explanation: The formula calculates the volume by subtracting the volume of the removed portion from the original cuboid volume.

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 residual values are less than or equal to their corresponding original dimensions. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cut Cuboid?
A: A Cut Cuboid is a three-dimensional geometric shape formed by cutting a portion from a regular cuboid, resulting in a shape with varying edge lengths.

Q2: Why divide by 6 in the formula?
The division by 6 accounts for the specific geometric relationship between the removed portion and the original cuboid volume calculation.

Q3: Can residual values be zero?
A: Yes, residual values can be zero, which would represent a complete cut along that dimension.

Q4: What units should be used?
A: The calculator uses meters for all dimensions, but the formula works with any consistent unit of measurement.

Q5: Are there limitations to this formula?
A: This formula assumes clean, straight cuts and may not be accurate for irregular cut shapes or curved surfaces.