1. What is Face Diagonal of Cube?

The Face Diagonal of a Cube is the distance between any pair of opposite corners on a particular square face of the Cube. It represents the longest straight line that can be drawn within a single face of the cube.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
• Insphere Radius of Cube — Radius of the sphere contained within the cube

Explanation: The formula establishes the relationship between the insphere radius and the face diagonal through geometric properties of the cube.

3. Importance of Face Diagonal Calculation

Details: Calculating the face diagonal is important in geometry, engineering, and architecture for determining spatial relationships, material requirements, and structural integrity in cube-based designs.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding face diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between insphere radius and cube side length?
A: The insphere radius equals half the side length of the cube (ri = a/2).

Q2: How is the face diagonal related to the side length?
A: Face diagonal = side length × √2.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to cubes due to their unique geometric properties.

Q4: What are practical applications of face diagonal calculation?
A: Used in construction, packaging design, 3D modeling, and spatial analysis where cube geometry is involved.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though practical measurements may have precision limitations.