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

Volume of Parallelepiped Formula:

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

Side C of Parallelepiped (Sc):

Angle Gamma of Parallelepiped (γ):

rad

Lateral Surface Area of Parallelepiped (LSA):

m²

Side B of Parallelepiped (Sb):

Angle Alpha of Parallelepiped (α):

rad

Angle Beta of Parallelepiped (β):

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, which is calculated using its side lengths and the angles between them.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( Sc \) — Side C of Parallelepiped (m)
\( \gamma \) — Angle Gamma of Parallelepiped (rad)
\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( Sb \) — Side B of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (rad)
\( \beta \) — Angle Beta of Parallelepiped (rad)

Explanation: This formula calculates the volume of a parallelepiped using trigonometric functions and geometric relationships between its sides and angles.

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 required values in appropriate units. Angles should be in radians. All values must be positive numbers within their valid ranges.

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.

Q2: Why are angles measured in radians?
A: Radians are the standard unit for angle measurement in mathematical calculations involving trigonometric functions.

Q3: Can I use degrees instead of radians?
A: No, the calculator requires angles in radians. Convert degrees to radians by multiplying by π/180.

Q4: What if I get a negative volume?
A: Volume should always be positive. A negative result indicates invalid input values or angles outside the valid range.

Q5: What are typical applications of this calculation?
A: This calculation is used in engineering design, architectural planning, material science, and physics problems involving three-dimensional space.