Perimeter of Parallelepiped given Volume, Side A and Side C Calculator

Perimeter of Parallelepiped Formula:

\[ P = 4 \times \left( Sa + \frac{V}{Sa \times Sc \times \sqrt{1 + (2 \times \cos(\angle\alpha) \times \cos(\angle\beta) \times \cos(\angle\gamma)) - (\cos(\angle\alpha)^2 + \cos(\angle\beta)^2 + \cos(\angle\gamma)^2)}} + Sc \right) \]

Side A of Parallelepiped (Sa):

Volume of Parallelepiped (V):

m³

Side C of Parallelepiped (Sc):

Angle Alpha of Parallelepiped (∠α):

rad

Angle Beta of Parallelepiped (∠β):

rad

Angle Gamma of Parallelepiped (∠γ):

rad

Perimeter of Parallelepiped (P):

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1. What is the Perimeter of Parallelepiped Formula?

The perimeter of a parallelepiped is calculated using a formula that considers side lengths, volume, and the angles between the sides. This specific formula calculates the perimeter given volume, side A, and side C measurements along with the three angles between the sides.

2. How Does the Calculator Work?

The calculator uses the perimeter formula:

Where:

\( P \) — Perimeter of Parallelepiped (m)
\( Sa \) — Side A of Parallelepiped (m)
\( V \) — Volume of Parallelepiped (m³)
\( Sc \) — Side C of Parallelepiped (m)
\( \angle\alpha \) — Angle Alpha of Parallelepiped (rad)
\( \angle\beta \) — Angle Beta of Parallelepiped (rad)
\( \angle\gamma \) — Angle Gamma of Parallelepiped (rad)

Explanation: The formula accounts for the geometric relationships between the sides, angles, and volume of the parallelepiped to calculate its total perimeter.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a parallelepiped is important in various engineering, architectural, and mathematical applications where understanding the boundary dimensions of three-dimensional objects is required.

4. Using the Calculator

Tips: Enter all measurements in consistent units (meters for lengths, cubic meters for volume, radians for angles). Ensure all values are positive and angles are within valid ranges (0 to π radians).

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 three angles needed for the calculation?
A: The three angles (alpha, beta, gamma) define the spatial relationships between the three pairs of sides in the parallelepiped, which affects its shape and perimeter.

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 an error or unexpected result?
A: Check that all input values are positive and that the angles are within valid ranges. Also verify that the combination of side lengths and volume is geometrically possible.

Q5: Are there any limitations to this formula?
A: This formula assumes a standard parallelepiped configuration and may not be applicable to degenerate or special cases where the mathematical operations become undefined.