Circumsphere Radius Of Disheptahedron Given Volume Calculator

Circumsphere Radius of Disheptahedron Formula:

\[ r_c = \left( \frac{3 \times V}{5 \times \sqrt{2}} \right)^{\frac{1}{3}} \]

Circumsphere Radius (r_c):

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1. What is the Circumsphere Radius of Disheptahedron?

The Circumsphere Radius of Disheptahedron is the radius of the sphere that contains the Disheptahedron in such a way that all the vertices of the Disheptahedron are touching the sphere. It is an important geometric property that helps in understanding the spatial dimensions of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \left( \frac{3 \times V}{5 \times \sqrt{2}} \right)^{\frac{1}{3}} \]

Where:

\( r_c \) — Circumsphere Radius (m)
\( V \) — Volume of Disheptahedron (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the circumsphere radius based on the volume of the disheptahedron, using the mathematical relationship between volume and the radius of the circumscribed sphere.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is crucial for understanding the spatial extent of the disheptahedron, which has applications in geometry, crystallography, and materials science where precise spatial measurements are required.

4. Using the Calculator

Tips: Enter the volume of the disheptahedron in cubic meters. The value must be positive and greater than zero. The calculator will compute the circumsphere radius using the established mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Disheptahedron?
A: A Disheptahedron is a polyhedron with specific geometric properties, though the exact definition may vary in different mathematical contexts.

Q2: Why is the square root of 2 used in the formula?
A: The square root of 2 appears in the formula due to the geometric relationships and symmetry properties inherent in the disheptahedron's structure.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the disheptahedron. Other polyhedra have different relationships between volume and circumsphere radius.

Q4: What are the units of measurement?
A: The volume should be in cubic meters (m³) and the resulting circumsphere radius will be in meters (m).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the given formula. The accuracy depends on the precision of the input volume value.