Height of Skewed Cuboid given Volume Calculator

Formula Used:

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

Volume of Skewed Cuboid (V):

m³

Length of Small Rectangle (lSmall):

Width of Small Rectangle (wSmall):

Width of Large Rectangle (wLarge):

Length of Large Rectangle (lLarge):

Height of Skewed Cuboid (h):

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1. What is the Height of Skewed Cuboid?

The Height of Skewed Cuboid is the vertical distance measured from base to the top of Skewed Cuboid. It represents the perpendicular distance between the larger rectangular base and the smaller rectangular top surface.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( h \) — Height of Skewed Cuboid (m)
\( V \) — Volume of Skewed Cuboid (m³)
\( l_{Small} \) — Length of Small Rectangle (m)
\( w_{Small} \) — Width of Small Rectangle (m)
\( w_{Large} \) — Width of Large Rectangle (m)
\( l_{Large} \) — Length of Large Rectangle (m)

Explanation: The formula calculates the height by dividing the volume by the average cross-sectional area of the skewed cuboid, accounting for the trapezoidal shape variations.

3. Importance of Height Calculation

Details: Calculating the height of a skewed cuboid is essential in various engineering and architectural applications, particularly when dealing with irregular prismatic structures where the top and bottom surfaces are rectangular but not parallel.

4. Using the Calculator

Tips: Enter all dimensions in meters and volume in cubic meters. Ensure all values are positive and the denominator doesn't equal zero. The calculator provides precise height measurement for skewed cuboid structures.

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 surfaces are rectangles of different sizes, and the lateral faces are trapezoids rather than rectangles.

Q2: When is this formula applicable?
A: This formula is used when you know the volume of a skewed cuboid and the dimensions of both the top and bottom rectangular surfaces, and need to find the perpendicular height.

Q3: What units should I use?
A: Use consistent units (preferably meters for length and cubic meters for volume) to ensure accurate results.

Q4: What if I get a division by zero error?
A: This occurs when the denominator equals zero, which typically happens with invalid dimension combinations. Check your input values.

Q5: Can this calculator handle decimal inputs?
A: Yes, the calculator supports decimal inputs with up to 4 decimal places precision for accurate calculations.