Height of Cut Cuboid given Volume Calculator

Formula Used:

\[ h = \frac{V + \frac{l_{Missing} \times h_{Missing} \times w_{Missing}}{6}}{l \times w} \]

Volume of Cut Cuboid (V):

m³

Missing Length of Cut Cuboid (lMissing):

Missing Height of Cut Cuboid (hMissing):

Missing Width of Cut Cuboid (wMissing):

Length of Cut Cuboid (l):

Width of Cut Cuboid (w):

Height of Cut Cuboid (h):

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1. What is the Height of Cut Cuboid Formula?

The Height of Cut Cuboid formula calculates the height of a cuboid when a portion has been cut off, using the volume and dimensions of the remaining shape along with the dimensions of the missing portion.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{V + \frac{l_{Missing} \times h_{Missing} \times w_{Missing}}{6}}{l \times w} \]

Where:

\( h \) — Height of Cut Cuboid (m)
\( V \) — Volume of Cut Cuboid (m³)
\( l_{Missing} \) — Missing Length of Cut Cuboid (m)
\( h_{Missing} \) — Missing Height of Cut Cuboid (m)
\( w_{Missing} \) — Missing Width of Cut Cuboid (m)
\( l \) — Length of Cut Cuboid (m)
\( w \) — Width of Cut Cuboid (m)

Explanation: The formula accounts for both the remaining volume and the volume of the missing portion to calculate the complete height dimension.

3. Importance of Height Calculation

Details: Accurate height calculation is crucial for determining the complete dimensions of cut cuboids in architectural, engineering, and manufacturing applications where partial volumes are involved.

4. Using the Calculator

Tips: Enter all dimensions in meters. Volume must be positive, and length/width must be greater than zero. Missing dimensions should be non-negative values.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cut Cuboid?
A: A Cut Cuboid is a three-dimensional shape formed when a portion of a complete cuboid has been removed or cut off.

Q2: Why is the missing portion divided by 6 in the formula?
A: The division by 6 accounts for the volumetric relationship between the missing triangular prism portion and the complete cuboid dimensions.

Q3: Can this formula be used for any type of cut?
A: This specific formula is designed for cuts that result in triangular prism missing portions. Different cut types may require different formulas.

Q4: What units should be used for input values?
A: All dimensions should be in consistent units (meters recommended). The calculator will output height in the same units.

Q5: What if I get a negative result?
A: Negative results are not physically possible for height. Check that all input values are positive and that the missing dimensions don't exceed the remaining dimensions.