Volume Of Parallelepiped Given Perimeter, Side A And Side B Calculator

Volume Of Parallelepiped Formula:

\[ V = S_a \times S_b \times (P/4-S_a-S_b) \times \sqrt{1+(2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma))-(\cos(\alpha)^2+\cos(\beta)^2+\cos(\gamma)^2)} \]

Side A of Parallelepiped:

Side B of Parallelepiped:

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 is calculated using the formula that considers three side lengths and the angles between them. This formula provides the three-dimensional space enclosed by the parallelepiped's surface.

2. How Does the Calculator Work?

The calculator uses the volume formula:

\[ V = S_a \times S_b \times (P/4-S_a-S_b) \times \sqrt{1+(2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma))-(\cos(\alpha)^2+\cos(\beta)^2+\cos(\gamma)^2)} \]

Where:

\( S_a \) — Side A length of the parallelepiped (m)
\( S_b \) — Side B length of the parallelepiped (m)
\( P \) — Perimeter of the parallelepiped (m)
\( \alpha \) — Angle Alpha between sides (rad)
\( \beta \) — Angle Beta between sides (rad)
\( \gamma \) — Angle Gamma between sides (rad)

Explanation: The formula accounts for the geometric properties of the parallelepiped, incorporating side lengths, perimeter, and the angles between the sides to calculate the volume.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining the capacity of three-dimensional spaces, structural engineering applications, and various geometric calculations in mathematics and physics.

4. Using the Calculator

Tips: Enter all side lengths in meters, perimeter in meters, and angles in radians. All values must be valid positive numbers with angles typically between 0 and π radians.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms, with opposite faces parallel and equal in area.

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

Q3: What are typical values for the angles?
A: In a rectangular parallelepiped (box), all angles are π/2 radians (90 degrees). Other parallelepipeds have angles that vary but are typically between 0 and π radians.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for all inputs with up to 4 decimal places precision.

Q5: What if I get a negative result?
A: Volume should always be positive. A negative result indicates invalid input values that don't form a valid parallelepiped.