1. What is the Edge Length of Cube given Circumsphere Radius Formula?

The formula calculates the edge length of a cube when the circumsphere radius is known. The circumsphere radius is the radius of the sphere that contains the cube with all vertices touching the sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• \( Circumsphere\ Radius\ of\ Cube \) — Radius of the sphere containing the cube

Explanation: The formula derives from the geometric relationship between a cube's edge length and the radius of its circumscribed sphere.

3. Importance of Edge Length Calculation

Details: Calculating edge length from circumsphere radius is essential in geometry, 3D modeling, and various engineering applications where spatial relationships need to be determined.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumsphere radius?
A: The circumsphere radius is the radius of the smallest sphere that can completely contain a cube, with all vertices of the cube touching the sphere's surface.

Q2: Why is the square root of 3 in the formula?
A: The square root of 3 appears due to the spatial diagonal relationship in a cube, where the diagonal equals the edge length multiplied by √3.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to cubes. Other polyhedrons have different relationships between edge length and circumsphere radius.

Q4: What are the units for the result?
A: The result will be in the same units as the input circumsphere radius (typically meters).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though the displayed result may be rounded for practical purposes.