First Partial Length of Bent Cuboid given Space Diagonal Calculator

Formula Used:

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

Space Diagonal of Bent Cuboid:

Second Partial Length of Bent Cuboid:

Height of Bent Cuboid:

First Partial Length of Bent Cuboid:

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1. What is First Partial Length of Bent Cuboid?

First Partial Length of Bent Cuboid is the outer edge of horizontal part of Bent Cuboid standing upright, it is equal to the length of first part of Bent Cuboid. It is an important geometric parameter in three-dimensional space calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( Space\ Diagonal \) — The line segment connecting two vertices that are not on the same face (m)
\( Second\ Partial\ Length \) — Outer edge of vertical part of Bent Cuboid standing upright (m)
\( Height \) — Distance between the lowest and highest points of Bent Cuboid (m)

Explanation: This formula is derived from the Pythagorean theorem applied in three-dimensional space, where the space diagonal forms the hypotenuse of a right-angled triangle with the three partial lengths as sides.

3. Importance of First Partial Length Calculation

Details: Accurate calculation of first partial length is crucial for geometric modeling, architectural design, and engineering applications involving bent cuboid structures. It helps in determining the complete dimensions and spatial relationships within the cuboid.

4. Using the Calculator

Tips: Enter space diagonal, second partial length, and height in meters. All values must be positive numbers. The calculator will compute the first partial length using the geometric relationship between these parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Bent Cuboid?
A: A Bent Cuboid is a three-dimensional geometric shape formed by bending a regular cuboid along one of its edges, creating two partial lengths.

Q2: How accurate is this calculation?
A: The calculation is mathematically precise when accurate input values are provided, as it's based on the fundamental Pythagorean theorem in three dimensions.

Q3: Can this formula be used for any cuboid?
A: This specific formula applies to bent cuboids where the space diagonal and the other two dimensions (second partial length and height) are known.

Q4: What units should I use?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit of measurement (cm, mm, inches, etc.).

Q5: What if I get a negative value under the square root?
A: A negative value indicates that the input values are not geometrically possible for a bent cuboid. Please verify your measurements.