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

Total Surface Area Of Parallelepiped Formula:

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

Volume of Parallelepiped (V):

m³

Side A of Parallelepiped (Sₐ):

Side C of Parallelepiped (S꜀):

Angle Alpha (α):

rad

Angle Beta (β):

rad

Angle Gamma (γ):

rad

Total Surface Area of Parallelepiped (TSA):

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1. What is the Total Surface Area of Parallelepiped?

The Total Surface Area of a Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped. It represents the sum of the areas of all six faces of this three-dimensional geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the total surface area by considering the volume, two sides, and all three angles of the parallelepiped, using trigonometric functions to account for the shape's orientation.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, heat transfer calculations, and structural design where the surface area of a parallelepiped shape needs to be determined.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, cubic meters for volume, and radians for angles). Ensure all values are positive and angles are 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. It's the 3D equivalent of a parallelogram.

Q2: Why are all three angles needed for the calculation?
A: All three angles (α, β, γ) are needed because they define the orientation of the faces relative to each other, which affects the surface area calculation.

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

Q4: What if I have different measurements?
A: This specific calculator requires volume, side A, side C, and all three angles. If you have different measurements, you might need a different formula or calculator.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the given inputs. The practical accuracy depends on the precision of your measurements.