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 represents the smallest sphere that can completely enclose the cube.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Cube (m)
• \( V \) — Volume of Cube (m³)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula derives from the relationship between the cube's volume and its spatial diagonal, which equals the diameter of the circumsphere.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry, 3D modeling, packaging design, and spatial analysis where understanding the minimal bounding sphere of a cube is necessary.

4. Using the Calculator

Tips: Enter the volume of the cube in cubic meters. The value must be positive (volume > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between cube side length and circumsphere radius?
A: For a cube with side length 'a', the circumsphere radius is \( \frac{\sqrt{3}}{2} \times a \).

Q2: How is this formula derived from cube geometry?
A: The spatial diagonal of a cube with side 'a' is \( a\sqrt{3} \), which equals the diameter of the circumsphere, making the radius \( \frac{a\sqrt{3}}{2} \).

Q3: Can this calculator handle different units?
A: The calculator uses cubic meters for volume and meters for radius. Convert other units to meters before calculation.

Q4: What's the difference between circumsphere and insphere?
A: Circumsphere touches all vertices, while insphere touches all faces of the cube.

Q5: Is this applicable to all cubes?
A: Yes, this formula works for all perfect cubes regardless of size.