Total Surface Area Of Parallelepiped Given Volume Side A And Side B Calculator

Formula Used:

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

Side A of Parallelepiped:

Side B of Parallelepiped:

Volume of Parallelepiped:

m³

Angle Alpha of Parallelepiped:

rad

Angle Beta of Parallelepiped:

rad

Angle Gamma of Parallelepiped:

rad

Total Surface Area of Parallelepiped:

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1. What is the Total Surface Area of Parallelepiped?

The total surface area of a parallelepiped is the sum of the areas of all its faces. It represents the total quantity of plane enclosed by the entire surface of the parallelepiped.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( S_a \) — Side A of Parallelepiped (m)
\( S_b \) — Side B of Parallelepiped (m)
\( V \) — Volume of Parallelepiped (m³)
\( \alpha \) — 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 geometric properties and trigonometric relationships between the sides and angles of the parallelepiped.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, heat transfer calculations, and structural analysis in engineering and architectural designs.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Side lengths and volume must be positive values. Angles should be entered in radians and must be positive.

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 required for this calculation?
A: The three angles (alpha, beta, gamma) define the spatial orientation and relationships between the three pairs of sides in the parallelepiped.

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

Q4: What if I get a negative value under the square root?
A: This indicates invalid input values that don't form a valid parallelepiped. Please check your input values.

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