Volume of Skewed Cuboid Calculator

Formula Used:

\[ V = (l_{Small} \times w_{Small} \times h) + (h \times (w_{Large} - w_{Small}) \times l_{Small}/2) + (h \times (l_{Large} - l_{Small}) \times w_{Small}/2) + ((l_{Large} - l_{Small}) \times (w_{Large} - w_{Small}) \times h/6) \]

Length of Small Rectangle:

Width of Small Rectangle:

Height:

Width of Large Rectangle:

Length of Large Rectangle:

Volume of Skewed Cuboid:

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1. What is the Volume of Skewed Cuboid?

A skewed cuboid is a three-dimensional shape with six rectangular faces where the top and bottom faces are rectangles of different sizes and are not parallel. The volume represents the total space enclosed within this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( l_{Small} \) — Length of small rectangle (m)
\( w_{Small} \) — Width of small rectangle (m)
\( h \) — Height of skewed cuboid (m)
\( w_{Large} \) — Width of large rectangle (m)
\( l_{Large} \) — Length of large rectangle (m)

Explanation: The formula calculates the volume by summing four components that account for the different geometric sections of the skewed cuboid.

3. Importance of Volume Calculation

Details: Calculating the volume of skewed cuboids is essential in various fields including architecture, engineering, packaging design, and 3D modeling where non-standard geometric shapes are encountered.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure that the large rectangle dimensions are greater than or equal to the small rectangle dimensions. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a skewed cuboid?
A: A skewed cuboid is a three-dimensional shape where the top and bottom rectangular faces are of different sizes and not parallel, creating a slanted appearance.

Q2: How is this different from a regular cuboid?
A: Unlike a regular cuboid where all angles are right angles and opposite faces are equal and parallel, a skewed cuboid has non-parallel top and bottom faces of different sizes.

Q3: What are practical applications of this calculation?
A: This calculation is used in architectural design, packaging optimization, storage container design, and any application involving irregular 3D shapes.

Q4: Are there any limitations to this formula?
A: The formula assumes the shape is a perfect skewed cuboid with rectangular faces. It may not be accurate for shapes with curved surfaces or irregular geometries.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert all measurements to meters before calculation or adjust the result accordingly.