Volume Of Octahedron Given Total Surface Area Calculator

Formula Used:

\[ Volume\ of\ Octahedron = \frac{\sqrt{2}}{3} \times \left( \sqrt{\frac{Total\ Surface\ Area\ of\ Octahedron}{2 \times \sqrt{3}}} \right)^3 \]

Volume of Octahedron:

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1. What is the Volume of Octahedron Formula?

The formula calculates the volume of a regular octahedron when given its total surface area. An octahedron is an eight-faced polyhedron where all faces are equilateral triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\sqrt{2}}{3} \times \left( \sqrt{\frac{TSA}{2 \times \sqrt{3}}} \right)^3 \]

Where:

\( V \) — Volume of Octahedron (m³)
\( TSA \) — Total Surface Area of Octahedron (m²)

Explanation: The formula derives the edge length from the surface area, then calculates the volume using the standard octahedron volume formula.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific applications where spatial measurements are required.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding volume.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octahedron?
A: A regular octahedron is a polyhedron with 8 equilateral triangular faces, 12 edges, and 6 vertices.

Q2: Why is the formula structured this way?
A: The formula first calculates the edge length from the surface area, then uses the standard volume formula V = (√2/3) × a³ where a is the edge length.

Q3: What units should I use?
A: Use consistent units. If surface area is in m², volume will be in m³. The calculator assumes metric units.

Q4: Can this calculator handle different units?
A: The calculator works with any consistent unit system, but the input must be in area units and the output will be in corresponding volume units.

Q5: What if I get an error or unexpected result?
A: Ensure you've entered a positive surface area value. Very large or very small values might be affected by computational precision limitations.