Height of Bent Cuboid given Space Diagonal Calculator

Formula Used:

\[ Height = \sqrt{Space Diagonal^2 - First Partial Length^2 - Second Partial Length^2} \]

Space Diagonal of Bent Cuboid:

First Partial Length of Bent Cuboid:

Second Partial Length of Bent Cuboid:

Height of Bent Cuboid:

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1. What is Height of Bent Cuboid given Space Diagonal?

The Height of Bent Cuboid given Space Diagonal is the vertical measurement of a bent cuboid calculated using its space diagonal and partial lengths. It represents the distance between the lowest and highest points when the cuboid is standing upright.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Height = \sqrt{Space Diagonal^2 - First Partial Length^2 - Second Partial Length^2} \]

Where:

\( Space Diagonal \) — The longest diagonal connecting opposite vertices of the bent cuboid (m)
\( First Partial Length \) — Outer edge of horizontal part of bent cuboid (m)
\( Second Partial Length \) — Outer edge of vertical part of bent cuboid (m)

Explanation: This formula applies the Pythagorean theorem in three dimensions to calculate the height component from the space diagonal and the two partial lengths.

3. Importance of Height Calculation

Details: Accurate height calculation is essential for determining the complete dimensions of bent cuboids in architectural design, engineering applications, and 3D modeling where precise spatial measurements are required.

4. Using the Calculator

Tips: Enter space diagonal and both partial lengths in meters. All values must be positive numbers, and the space diagonal must be greater than the square root of the sum of squares of the partial lengths.

5. Frequently Asked Questions (FAQ)

Q1: What is a bent cuboid?
A: A bent cuboid is a three-dimensional shape formed by bending a rectangular cuboid along one of its edges, creating two connected rectangular sections.

Q2: Why is the square root function used in this formula?
A: The square root function is used to solve for the height component in the three-dimensional Pythagorean theorem applied to the space diagonal.

Q3: What units should be used for input values?
A: All input values should be in consistent units (typically meters), and the result will be in the same units.

Q4: What if the calculation results in a negative value under the square root?
A: A negative value indicates invalid input where the space diagonal is shorter than the combined effect of partial lengths, which is geometrically impossible.

Q5: Can this formula be used for regular cuboids?
A: Yes, for regular cuboids, the partial lengths would correspond to the length and width dimensions.