1. What is Volume Of Cube Given Insphere Radius?

The Volume of Cube given Insphere Radius calculates the total three-dimensional space enclosed by a cube when the radius of its inscribed sphere (insphere) is known. The insphere touches all faces of the cube at their centers.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of the cube (m³)
• \( r_i \) — Insphere radius of the cube (m)

Explanation: Since the insphere touches all faces of the cube, its diameter equals the side length of the cube. Therefore, the side length is twice the insphere radius, and volume is side length cubed.

3. Importance of Volume Calculation

Details: Calculating volume from insphere radius is important in geometry, architecture, and engineering where sphere-cube relationships are involved. It helps in material estimation and spatial planning.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding cube volume.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between insphere radius and cube side length?
A: The cube's side length is exactly twice the insphere radius (s = 2 × r_i).

Q2: Can this formula be used for any cube?
A: Yes, this formula applies to all perfect cubes where an insphere can be inscribed.

Q3: What are the units for the result?
A: The volume is in cubic meters (m³) if radius is in meters. Ensure consistent units.

Q4: What if I have the circumsphere radius instead?
A: Different formulas apply for circumsphere radius. This calculator specifically uses insphere radius.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cubes with perfect inspheres.