Volume of Truncated Cuboid Calculator

Volume of Truncated Cuboid Formula:

\[ V = (l \times h \times w) - \frac{(h - h_{Short}) \times (w - w_{Short}) \times l}{2} \]

Length of Truncated Cuboid:

Height of Truncated Cuboid:

Width of Truncated Cuboid:

Shortened Height of Truncated Cuboid:

Shortened Width of Truncated Cuboid:

Volume of Truncated Cuboid:

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1. What is the Volume of Truncated Cuboid?

The Volume of Truncated Cuboid is the total quantity of three dimensional space enclosed by the surface of a Truncated Cuboid. It represents the capacity or space occupied by this geometric shape.

2. How Does the Calculator Work?

The calculator uses the Volume of Truncated Cuboid formula:

\[ V = (l \times h \times w) - \frac{(h - h_{Short}) \times (w - w_{Short}) \times l}{2} \]

Where:

\( V \) — Volume of Truncated Cuboid (m³)
\( l \) — Length of Truncated Cuboid (m)
\( h \) — Height of Truncated Cuboid (m)
\( w \) — Width of Truncated Cuboid (m)
\( h_{Short} \) — Shortened Height of Truncated Cuboid (m)
\( w_{Short} \) — Shortened Width of Truncated Cuboid (m)

Explanation: The formula calculates the full cuboid volume and subtracts the volume of the truncated triangular prism portion.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining material requirements, storage capacity, structural design, and various engineering applications involving truncated cuboid shapes.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure that shortened dimensions are less than or equal to the corresponding full dimensions. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Cuboid?
A: A Truncated Cuboid is a cuboid that has been cut or truncated, typically with one corner removed, creating a shape with five rectangular faces and one triangular face.

Q2: What units should I use for the inputs?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as long as all inputs are in the same unit.

Q3: Can the shortened dimensions be zero?
A: Yes, if both shortened dimensions are zero, the shape becomes a full cuboid, and the formula simplifies to V = l × h × w.

Q4: What if the shortened dimensions are larger than the full dimensions?
A: The shortened dimensions must be less than or equal to the corresponding full dimensions. The calculator will not produce valid results if this condition is violated.

Q5: Where is this calculation commonly used?
A: This calculation is used in architecture, construction, packaging design, and manufacturing where truncated cuboid shapes are encountered.