Total Surface Area of Trirectangular Tetrahedron given Volume, Second and Third Right Angle Edge Calculator

Formula Used:

\[ TSA = \frac{le(Right2) \times le(Right3)}{2} + \frac{3 \times V}{le(Right3)} + \frac{3 \times V}{le(Right2)} + \frac{3 \times V}{h} \]

Second RA Edge of Trirectangular Tetrahedron:

Third RA Edge of Trirectangular Tetrahedron:

Volume of Trirectangular Tetrahedron:

m³

Height of Trirectangular Tetrahedron:

Total Surface Area of Trirectangular Tetrahedron:

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1. What is Total Surface Area of Trirectangular Tetrahedron?

Total Surface Area of Trirectangular Tetrahedron is the total quantity of plane enclosed by the entire surface of the Trirectangular Tetrahedron. It represents the sum of the areas of all four triangular faces of the tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{le(Right2) \times le(Right3)}{2} + \frac{3 \times V}{le(Right3)} + \frac{3 \times V}{le(Right2)} + \frac{3 \times V}{h} \]

Where:

\( TSA \) — Total Surface Area of Trirectangular Tetrahedron (m²)
\( le(Right2) \) — Second RA Edge of Trirectangular Tetrahedron (m)
\( le(Right3) \) — Third RA Edge of Trirectangular Tetrahedron (m)
\( V \) — Volume of Trirectangular Tetrahedron (m³)
\( h \) — Height of Trirectangular Tetrahedron (m)

Explanation: This formula calculates the total surface area by summing the areas of all four triangular faces of the trirectangular tetrahedron.

3. Importance of Total Surface Area Calculation

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

4. Using the Calculator

Tips: Enter all values in meters and cubic meters respectively. All input values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Trirectangular Tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron with three faces meeting at one vertex that are mutually perpendicular to each other.

Q2: Why are there three different right angle edges?
A: The three right angle edges are the mutually perpendicular edges that meet at the vertex where the three right angles are located.

Q3: Can this formula be used for any tetrahedron?
A: No, this specific formula is designed specifically for trirectangular tetrahedrons with the given parameters.

Q4: What units should I use for the inputs?
A: All length measurements should be in meters, and volume should be in cubic meters for consistent results.

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