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

Volume of Parallelepiped Formula:

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

Side A of Parallelepiped:

Side B of Parallelepiped:

Total Surface Area of Parallelepiped:

m²

Angle Alpha of Parallelepiped:

Angle Beta of Parallelepiped:

Angle Gamma of Parallelepiped:

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 of a parallelepiped represents the amount of three-dimensional space it occupies, calculated using its side lengths, angles, and total surface area.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the volume of a parallelepiped using two side lengths, the total surface area, and the three angles between the sides.

3. Importance of Volume Calculation

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

4. Using the Calculator

Tips: Enter all side lengths in meters, total surface area in square meters, and angles in degrees. All values must be positive and angles should be between 0 and 180 degrees.

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: How is this formula different from the standard volume formula?
A: This formula uses the total surface area and angles to calculate volume, unlike the standard formula which typically uses the scalar triple product of vectors.

Q3: What are the typical applications of parallelepiped volume calculation?
A: It's used in crystallography, engineering design, architecture, and any field dealing with three-dimensional space calculations.

Q4: Are there any limitations to this formula?
A: The formula assumes the parallelepiped is a valid geometric shape with appropriate angle relationships between sides.

Q5: Can this calculator handle different units?
A: The calculator uses meters for length and square meters for area. Convert other units to these before calculation.