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

Formula Used:

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

Volume of Parallelepiped (V):

m³

Side B of Parallelepiped (S_b):

Side C of Parallelepiped (S_c):

Angle Alpha (α):

Angle Beta (β):

Angle Gamma (γ):

Perimeter of Parallelepiped (P):

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1. What is the Perimeter of Parallelepiped?

The perimeter of a parallelepiped is the total distance around the edge of the three-dimensional figure. It represents the sum of all the edges of the parallelepiped.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( P \) — Perimeter of Parallelepiped (m)
\( V \) — Volume of Parallelepiped (m³)
\( S_b \) — Side B of Parallelepiped (m)
\( S_c \) — Side C of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (radians)
\( \beta \) — Angle Beta of Parallelepiped (radians)
\( \gamma \) — Angle Gamma of Parallelepiped (radians)

Explanation: This formula calculates the perimeter based on the volume, two sides, and the three angles between the sides at the vertices.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a parallelepiped is important in various engineering and architectural applications where the total edge length needs to be determined for material estimation, structural analysis, or design purposes.

4. Using the Calculator

Tips: Enter volume in cubic meters, side lengths in meters, and angles in degrees. All values must be positive and angles should be between 0-180 degrees.

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 (α, β, γ) define the spatial relationships between the three sides at the vertices, which are essential for accurately calculating the perimeter from the given volume.

Q3: Can this formula be used for any parallelepiped?
A: Yes, this formula applies to all parallelepipeds, including rectangular ones (where all angles are 90 degrees).

Q4: What are the units of measurement?
A: Volume should be in cubic meters (m³), sides in meters (m), and angles in degrees. The result will be in meters (m).

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