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

Volume of Parallelepiped Formula:

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

Side A of Parallelepiped:

Angle Alpha of Parallelepiped:

Lateral Surface Area of Parallelepiped:

m²

Side B of Parallelepiped:

Angle Gamma of Parallelepiped:

Angle Beta of Parallelepiped:

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, angles, and lateral surface area. This specific formula calculates volume when given side A, side B, lateral surface area, and the three angles between sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( V \) — Volume of Parallelepiped (m³)
\( S_a \) — Side A of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (degrees)
\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( S_b \) — Side B of Parallelepiped (m)
\( \gamma \) — Angle Gamma of Parallelepiped (degrees)
\( \beta \) — Angle Beta of Parallelepiped (degrees)

Explanation: The formula calculates the volume by considering the geometric relationships between the sides, angles, and lateral surface area 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 three-dimensional space calculations are required.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Angles should be between 0 and 180 degrees. All values must be positive numbers.

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 the calculation?
A: The three angles (alpha, beta, gamma) define the orientation of the three pairs of parallel faces relative to each other in 3D space.

Q3: What is lateral surface area?
A: Lateral surface area is the area of all the side faces excluding the top and bottom faces of the parallelepiped.

Q4: Can this formula be used for any parallelepiped?
A: Yes, this formula works for any parallelepiped as long as all the required parameters are known.

Q5: What are the units of measurement?
A: Lengths should be in meters (m), angles in degrees (°), area in square meters (m²), and volume in cubic meters (m³).