Residual Height of Cut Cuboid given Width to Height Slant Line Calculator

Formula Used:

\[ \text{Residual Height of Cut Cuboid} = \text{Height of Cut Cuboid} - \sqrt{\text{WH Slant Line of Cut Cuboid}^2 - \text{Missing Width of Cut Cuboid}^2} \] \[ h_{\text{Residual}} = h - \sqrt{l_{\text{Slant(WH)}}^2 - w_{\text{Missing}}^2} \]

Residual Height of Cut Cuboid:

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1. What is Residual Height of Cut Cuboid?

The Residual Height of Cut Cuboid is the remaining part of the cut off height of Cut Cuboid. It represents the vertical dimension that remains after a portion has been removed from the original cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{\text{Residual}} = h - \sqrt{l_{\text{Slant(WH)}}^2 - w_{\text{Missing}}^2} \]

Where:

\( h_{\text{Residual}} \) — Residual Height of Cut Cuboid (m)
\( h \) — Height of Cut Cuboid (m)
\( l_{\text{Slant(WH)}} \) — WH Slant Line of Cut Cuboid (m)
\( w_{\text{Missing}} \) — Missing Width of Cut Cuboid (m)

3. Formula Explanation

Mathematical Basis: The formula applies the Pythagorean theorem to calculate the residual height based on the slant line and missing width dimensions of the cut cuboid.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure that the WH Slant Line is greater than the Missing Width to obtain a valid result. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for input values?
A: All input values should be in meters (m) for consistent results.

Q2: What if I get a negative result?
A: A negative result indicates that the input values may be inconsistent or that the missing width is larger than what the geometry allows.

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q4: What is the practical application of this calculation?
A: This calculation is useful in geometry, engineering, and construction where cuboid shapes are cut and residual dimensions need to be determined.

Q5: How accurate are the results?
A: The results are accurate to 6 decimal places, providing precise measurements for engineering applications.