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

Volume of Parallelepiped Formula:

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

Side A of Parallelepiped:

Side C of Parallelepiped:

Total Surface Area:

m²

Angle Alpha (α):

rad

Angle Beta (β):

rad

Angle Gamma (γ):

rad

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, total surface area, and the angles between sides. This formula provides an accurate measurement of the three-dimensional space enclosed by the parallelepiped.

2. How Does the Calculator Work?

The calculator uses the volume formula:

Where:

\( S_a \) — Side A length (meters)
\( S_c \) — Side C length (meters)
\( TSA \) — Total Surface Area (square meters)
\( \alpha \) — Angle Alpha (radians)
\( \beta \) — Angle Beta (radians)
\( \gamma \) — Angle Gamma (radians)

Explanation: The formula accounts for the geometric relationships between the sides, angles, and total surface area to compute the volume accurately.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for various applications including engineering design, architectural planning, material estimation, and scientific research involving three-dimensional spaces.

4. Using the Calculator

Tips: Enter all side lengths in meters, total surface area in square meters, and angles in radians. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It's a polyhedron with parallelogram faces.

Q2: Why are angles measured in radians?
A: Trigonometric functions in mathematical formulas typically use radians for more accurate calculations in advanced mathematics and physics.

Q3: Can I use degrees instead of radians?
A: The calculator requires radians. Convert degrees to radians by multiplying by π/180.

Q4: What if I get a negative result?
A: Volume cannot be negative. Check your input values, particularly ensure angles are within valid ranges (0 to π radians).

Q5: Are there any limitations to this formula?
A: This formula assumes standard parallelepiped geometry and may not apply to irregular or deformed shapes.