Volume of Parallelepiped Given Perimeter, Side B and Side C Calculator

Volume of Parallelepiped Formula:

\[ V = S_b \times S_c \times \left(\frac{P}{4} - S_b - S_c\right) \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos^2(\alpha) + \cos^2(\beta) + \cos^2(\gamma))} \]

Side B of Parallelepiped:

Side C of Parallelepiped:

Perimeter of Parallelepiped:

Angle Alpha of Parallelepiped:

rad

Angle Beta of Parallelepiped:

rad

Angle Gamma of Parallelepiped:

rad

Volume of Parallelepiped:

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1. What is the Volume of Parallelepiped Formula?

The volume of a parallelepiped can be calculated using the formula that incorporates side lengths, perimeter, and the angles between sides. This formula provides an accurate measurement of the three-dimensional space enclosed by the parallelepiped.

2. How Does the Calculator Work?

The calculator uses the volume formula:

Where:

\( S_b \) — Side B of Parallelepiped (m)
\( S_c \) — Side C of Parallelepiped (m)
\( P \) — Perimeter of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (rad)
\( \beta \) — Angle Beta of Parallelepiped (rad)
\( \gamma \) — Angle Gamma of Parallelepiped (rad)

Explanation: The formula accounts for the geometric properties of the parallelepiped, including side lengths and the angles between them, to calculate the enclosed volume.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for various applications in geometry, engineering, and physics, including determining capacity, material requirements, and structural analysis.

4. Using the Calculator

Tips: Enter all side lengths in meters, perimeter in meters, and angles in radians. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It's a polyhedron with parallel opposite faces.

Q2: Why are angles measured in radians?
A: Radians are the standard unit of angular measurement in mathematical calculations, particularly in trigonometric functions.

Q3: What if I have angles in degrees?
A: Convert degrees to radians by multiplying by π/180 (approximately 0.0174533) before entering them into the calculator.

Q4: Are there any limitations to this formula?
A: This formula assumes a standard parallelepiped shape and may not be accurate for irregular or deformed parallelepipeds.

Q5: Can this calculator be used for other polyhedrons?
A: No, this specific formula is designed only for calculating the volume of parallelepipeds.