Volume Of Parallelepiped Given Total Surface Area, Side B And Side C Calculator

Volume Of Parallelepiped Formula:

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

Side B of Parallelepiped:

Side C of Parallelepiped:

Total Surface Area:

m²

Angle Alpha:

rad

Angle Beta:

rad

Angle Gamma:

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 using side lengths and angles between them.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the volume of a parallelepiped using side lengths B and C, 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 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 a polyhedron with parallelogram faces.

Q2: Why are three angles needed for the calculation?
A: The three angles (alpha, beta, gamma) define the spatial relationships between the sides of the parallelepiped, which are necessary to accurately calculate its volume.

Q3: Can I use degrees instead of radians?
A: The calculator requires angles in radians. To convert degrees to radians, multiply by π/180 (approximately 0.0174533).

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

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy of the result depends on the precision of your measurements.