Third Right Angle Edge of Trirectangular Tetrahedron given Volume Calculator

Formula Used:

\[ \text{Third RA Edge} = \frac{6 \times \text{Volume}}{\text{First RA Edge} \times \text{Second RA Edge}} \]

Volume of Trirectangular Tetrahedron:

m³

First RA Edge of Trirectangular Tetrahedron:

Second RA Edge of Trirectangular Tetrahedron:

Third RA Edge of Trirectangular Tetrahedron:

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1. What is the Third Right Angle Edge of Trirectangular Tetrahedron?

The Third Right Angle Edge of a Trirectangular Tetrahedron is the third edge out of the three mutually perpendicular edges that form the right angles in this special type of tetrahedron where three faces meet at right angles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Third RA Edge} = \frac{6 \times \text{Volume}}{\text{First RA Edge} \times \text{Second RA Edge}} \]

Where:

Volume - Total volume of the trirectangular tetrahedron (m³)
First RA Edge - First mutually perpendicular edge (m)
Second RA Edge - Second mutually perpendicular edge (m)

Explanation: This formula derives from the volume calculation of a trirectangular tetrahedron and allows solving for the third edge when volume and the other two edges are known.

3. Importance of Third RA Edge Calculation

Details: Calculating the third right angle edge is essential for geometric analysis, structural engineering applications, and understanding the spatial properties of trirectangular tetrahedrons in 3D modeling and computational geometry.

4. Using the Calculator

Tips: Enter the volume in cubic meters, and both first and second RA edges in meters. All 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 where three faces meet at right angles, forming three mutually perpendicular edges.

Q2: Can this formula be used for any tetrahedron?
A: No, this specific formula applies only to trirectangular tetrahedrons where three edges are mutually perpendicular.

Q3: What are the units for the result?
A: The result is in meters (m), consistent with the input units for the edges.

Q4: What if two edges are zero?
A: The calculator requires all inputs to be positive numbers greater than zero. Zero values are not valid for this calculation.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of trirectangular tetrahedrons, assuming precise input values.