Volume of Parallelepiped Given Lateral Surface Area, Side A and Side C Calculator

Formula Used:

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

Lateral Surface Area of Parallelepiped:

m²

Side A of Parallelepiped:

Side C 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?

A parallelepiped is a three-dimensional figure formed by six parallelograms. The volume represents the amount of space enclosed within this geometric shape, calculated based on its lateral surface area, side lengths, and angles between them.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( V \) — Volume of Parallelepiped (m³)
\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( Sa \) — Side A of Parallelepiped (m)
\( Sc \) — Side C of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (rad)
\( \beta \) — Angle Beta of Parallelepiped (rad)
\( \gamma \) — Angle Gamma of Parallelepiped (rad)

Explanation: The formula calculates volume using trigonometric functions to account for the angular relationships between the sides of the parallelepiped.

3. Importance of Volume Calculation

Details: Calculating the volume of a parallelepiped is essential in various fields including engineering, architecture, and physics, where understanding the capacity or space occupied by three-dimensional objects is crucial.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, square meters for area, radians for angles). Ensure all values are positive and angles are in valid ranges for trigonometric functions.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure with six faces, each of which is a parallelogram. It's the 3D equivalent of a parallelogram.

Q2: Why are trigonometric functions used in this calculation?
A: Trigonometric functions account for the angular relationships between the sides, which affect the overall volume of the shape.

Q3: Can I use degrees instead of radians?
A: The calculator requires angles in radians. To convert degrees to radians, multiply by π/180.

Q4: What are typical applications of parallelepiped volume calculations?
A: These calculations are used in crystallography, packaging design, structural engineering, and any field dealing with 3D space optimization.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect parallelepipeds. Real-world applications may require considering material thickness and other practical factors.