Volume Of Deltoidal Icositetrahedron Given Insphere Radius Calculator

Formula Used:

\[ V = \frac{2}{7} \times \sqrt{292 + 206 \times \sqrt{2}} \times \left( \frac{r_i}{\sqrt{\frac{22 + 15 \times \sqrt{2}}{34}}} \right)^3 \]

Volume of Deltoidal Icositetrahedron:

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1. What is Volume of Deltoidal Icositetrahedron?

The Volume of Deltoidal Icositetrahedron is the quantity of three dimensional space enclosed by the entire surface of Deltoidal Icositetrahedron. It is a Catalan solid with 24 deltoid faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{2}{7} \times \sqrt{292 + 206 \times \sqrt{2}} \times \left( \frac{r_i}{\sqrt{\frac{22 + 15 \times \sqrt{2}}{34}}} \right)^3 \]

Where:

\( V \) — Volume of Deltoidal Icositetrahedron (m³)
\( r_i \) — Insphere Radius of Deltoidal Icositetrahedron (m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the volume based on the insphere radius, incorporating mathematical constants and square roots to derive the precise volume measurement.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including mathematics, engineering, architecture, and 3D modeling. It helps in understanding spatial relationships and material requirements.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero. The calculator will compute the volume using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoid (kite-shaped) faces, 26 vertices, and 48 edges.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the sphere that is contained by the Deltoidal Icositetrahedron such that all faces just touch the sphere.

Q3: Why are there square roots in the formula?
A: The square roots are mathematical constants derived from the geometric properties of the Deltoidal Icositetrahedron and are necessary for precise volume calculation.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert the insphere radius to meters before calculation.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, providing accurate volume measurements for the specified insphere radius.