Side B of Parallelepiped Calculator

Formula Used:

\[ Sb = \frac{V}{Sa \times Sc \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)}} \]

Volume of Parallelepiped:

m³

Side A of Parallelepiped:

Side C of Parallelepiped:

Angle Alpha of Parallelepiped:

Angle Beta of Parallelepiped:

Angle Gamma of Parallelepiped:

Side B of Parallelepiped:

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1. What is Side B of Parallelepiped?

Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped. It is one of the fundamental dimensions used to define the geometry of a parallelepiped, along with sides A and C and the angles between them.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Sb = \frac{V}{Sa \times Sc \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)}} \]

Where:

\( Sb \) — Side B of Parallelepiped (m)
\( V \) — Volume of Parallelepiped (m³)
\( Sa \) — Side A of Parallelepiped (m)
\( Sc \) — Side C of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (radians)
\( \beta \) — Angle Beta of Parallelepiped (radians)
\( \gamma \) — Angle Gamma of Parallelepiped (radians)

Explanation: This formula calculates the length of side B based on the volume of the parallelepiped and the other two sides, taking into account the angles between the sides.

3. Importance of Side B Calculation

Details: Calculating side B is essential for understanding the complete geometry of a parallelepiped. It helps in various applications including structural engineering, crystallography, and 3D modeling where precise dimensional relationships are crucial.

4. Using the Calculator

Tips: Enter all values in appropriate units. Volume should be in cubic meters, sides in meters, and angles in degrees. All values must be positive numbers with angles between 0-180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It's the 3D equivalent of a parallelogram.

Q2: Why are three angles needed for this calculation?
A: The three angles (alpha, beta, gamma) define the spatial relationships between the three sides of the parallelepiped, which affects its volume and shape.

Q3: Can this formula be used for any type of parallelepiped?
A: Yes, this formula applies to all parallelepipeds, including rectangular ones (where all angles are 90 degrees).

Q4: What if I have the lengths of all three sides but need the volume?
A: The formula can be rearranged to calculate volume: \( V = Sa \times Sb \times Sc \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)} \)

Q5: Are there any limitations to this calculation?
A: The formula assumes the angles are measured in radians internally (converted from degrees) and that the input values form a valid parallelepiped geometry.