Volume Of Cut Cuboid Given Length To Width Slant Line Calculator

Formula Used:

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

Length of Cut Cuboid:

Height of Cut Cuboid:

Width of Cut Cuboid:

Missing Length of Cut Cuboid:

Missing Height of Cut Cuboid:

LW Slant Line 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 the cuboid after a portion has been cut off.

2. How Does the Calculator Work?

The calculator uses the formula:

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

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)
\( h_{Missing} \) — Missing Height of Cut Cuboid (m)
\( l_{Slant(LW)} \) — LW Slant Line of Cut Cuboid (m)

Explanation: The formula calculates the volume by subtracting the volume of the cut-off portion 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 utilization in various engineering and architectural applications.

4. Using the Calculator

Tips: Enter all dimensions in meters. All values must be positive numbers. Ensure the LW Slant Line is greater than the Missing Length for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cut Cuboid?
A: A Cut Cuboid is a cuboid that has a portion cut off from one of its corners, creating a slanted surface.

Q2: Why is the square root function used in the formula?
A: The square root function calculates the missing dimension needed to determine the volume of the cut-off triangular prism portion.

Q3: What are the units of measurement?
A: All inputs should be in meters (m), and the result will be in cubic meters (m³).

Q4: What if the LW Slant Line is smaller than the Missing Length?
A: The calculation would involve the square root of a negative number, which is not valid in real numbers. Ensure the LW Slant Line is always greater than the Missing Length.

Q5: Can this calculator be used for other shapes?
A: No, this calculator is specifically designed for calculating the volume of a cut cuboid with the given parameters.