1. What is Circumsphere Radius of Cube?

Circumsphere Radius of Cube is the radius of the sphere that contains the Cube in such a way that all the vertices of the Cube are touching the sphere. It represents the distance from the center of the cube to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Cube (m)
• \( r_i \) — Insphere Radius of Cube (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula establishes the mathematical relationship between the circumsphere radius and insphere radius of a cube, where the circumsphere radius is exactly √3 times the insphere radius.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and engineering applications where understanding the spatial dimensions and bounding sphere of a cube is necessary for design, analysis, and optimization purposes.

4. Using the Calculator

Tips: Enter the insphere radius of the cube in meters. The value must be positive and greater than zero. The calculator will compute the corresponding circumsphere radius using the mathematical relationship between these two geometric properties.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumsphere radius and cube side length?
A: The circumsphere radius is equal to \( \frac{\sqrt{3}}{2} \times \) side length of the cube.

Q2: How is insphere radius related to cube side length?
A: The insphere radius is equal to \( \frac{1}{2} \times \) side length of the cube.

Q3: Why is the circumsphere radius √3 times the insphere radius?
A: This relationship comes from the geometric properties of a cube, where the distance from center to vertex (circumsphere) is √3 times the distance from center to face (insphere).

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cubes. Other polyhedra have different relationships between their circumsphere and insphere radii.

Q5: What are practical applications of circumsphere radius calculation?
A: Applications include 3D modeling, game development, architectural design, packaging optimization, and any field requiring spatial analysis of cubic structures.