1. What is Circumsphere Radius of Cube?

The Circumsphere Radius of a 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's 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)
• \( r_{i(cylinder)} \) — Inscribed Cylinder Radius of Cube (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula shows the direct proportional relationship between the circumsphere radius and the inscribed cylinder radius of a cube, with the constant of proportionality being √3.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and various engineering applications where understanding the spatial relationships of cubic structures is necessary.

4. Using the Calculator

Tips: Enter the inscribed cylinder radius of the cube in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between cube side length and circumsphere radius?
A: The circumsphere radius equals half the space diagonal of the cube: \( r_c = \frac{\sqrt{3}}{2} \times a \), where a is the side length.

Q2: How is the inscribed cylinder radius related to cube side length?
A: The inscribed cylinder radius equals half the side length: \( r_{i(cylinder)} = \frac{a}{2} \).

Q3: Can this formula be derived from basic principles?
A: Yes, by considering the geometry of a cube and the relationships between its various dimensions.

Q4: What are practical applications of this calculation?
A: Used in packaging design, architecture, 3D modeling, and any field dealing with cubic structures and their containing spheres.

Q5: Does this formula work for all cubes?
A: Yes, this relationship holds true for all perfect cubes regardless of size.