Volume of Trirectangular Tetrahedron given Third Base and Third Right Angle Edge Calculator

Formula Used:

\[ V = \frac{\sqrt{le(Base3)^2 - le(Right3)^2} \times le(Right2) \times le(Right3)}{6} \]

Third Base Edge of Trirectangular Tetrahedron:

Third RA Edge of Trirectangular Tetrahedron:

Second RA Edge of Trirectangular Tetrahedron:

Volume of Trirectangular Tetrahedron:

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1. What is the Volume of Trirectangular Tetrahedron?

The Volume of Trirectangular Tetrahedron is the total quantity of three-dimensional space enclosed by the surface of the Trirectangular Tetrahedron. A trirectangular tetrahedron is a tetrahedron where three faces meet at right angles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\sqrt{le(Base3)^2 - le(Right3)^2} \times le(Right2) \times le(Right3)}{6} \]

Where:

\( le(Base3) \) — Third Base Edge of Trirectangular Tetrahedron (m)
\( le(Right3) \) — Third RA Edge of Trirectangular Tetrahedron (m)
\( le(Right2) \) — Second RA Edge of Trirectangular Tetrahedron (m)

Explanation: This formula calculates the volume of a trirectangular tetrahedron using the Pythagorean theorem relationship between the base edge and right angle edge, combined with the other perpendicular edges.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in determining capacity, material requirements, and spatial relationships.

4. Using the Calculator

Tips: Enter all three edge measurements in meters. The Third Base Edge must be greater than the Third RA Edge for the calculation to be valid. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a trirectangular tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron with three faces meeting at right angles, forming three mutually perpendicular edges.

Q2: Why must the Third Base Edge be greater than the Third RA Edge?
A: This requirement comes from the Pythagorean theorem used in the formula, where the square root operation requires a positive value inside.

Q3: What are the units of measurement for the result?
A: The volume is calculated in cubic meters (m³), which is the standard SI unit for volume.

Q4: Can this formula be used for any tetrahedron?
A: No, this specific formula applies only to trirectangular tetrahedrons with the given edge relationships.

Q5: How accurate is the calculation?
A: The calculation provides results with 6 decimal places of precision, which is sufficient for most practical applications.