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

Formula Used:

\[ TSA = \frac{le_{Right2} \times le_{Right1}}{2} + \frac{3V}{le_{Right1}} + \frac{3V}{le_{Right2}} + \frac{3V}{h} \]

First RA Edge of Trirectangular Tetrahedron:

Second 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 the Total Surface Area of Trirectangular Tetrahedron?

The Total Surface Area of a Trirectangular Tetrahedron is the total quantity of plane enclosed by the entire surface of the Trirectangular Tetrahedron. It is calculated using the formula that incorporates the three mutually perpendicular edges and the volume of the tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{le_{Right2} \times le_{Right1}}{2} + \frac{3V}{le_{Right1}} + \frac{3V}{le_{Right2}} + \frac{3V}{h} \]

Where:

\( le_{Right1} \) — First right angle edge of the tetrahedron (m)
\( le_{Right2} \) — Second right angle edge of the tetrahedron (m)
\( V \) — Volume of the tetrahedron (m³)
\( h \) — Height of the tetrahedron (m)

Explanation: The formula accounts for all four triangular faces of the tetrahedron, with each term representing the area of one face.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is important in various applications including material science, architecture, and engineering where surface coverage or coating requirements need to be determined.

4. Using the Calculator

Tips: Enter all values in meters and cubic meters. Ensure all values are positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Trirectangular Tetrahedron?
A: A Trirectangular Tetrahedron is a tetrahedron where three faces meet at right angles at one vertex.

Q2: Why are there three different terms with volume in the formula?
A: Each term represents the area of one of the three faces that contain the right angles, calculated using the volume and the respective edge lengths.

Q3: 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.

Q4: Can this formula be used for any tetrahedron?
A: No, this specific formula applies only to trirectangular tetrahedrons where three edges meet at right angles.

Q5: What if I have measurements in different units?
A: Convert all measurements to consistent units (preferably meters and cubic meters) before using the calculator.