1. What is the Insphere Radius of Cube?

The Insphere Radius of a Cube is the radius of the largest sphere that can fit entirely within the cube, touching all six faces. It represents the distance from the center of the cube to any of its faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere radius of the cube
• \( LSA \) — Lateral surface area of the cube

Explanation: The formula derives from the relationship between the lateral surface area and the side length of the cube, and the fact that the insphere radius is half the side length.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry, material science, and engineering applications where spherical objects need to fit perfectly within cubic containers or spaces.

4. Using the Calculator

Tips: Enter the lateral surface area of the cube in square meters. The value must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

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

Q2: How is lateral surface area related to side length?
A: Lateral surface area equals 4 times the square of the side length (LSA = 4a²).

Q3: What are typical applications of insphere radius calculation?
A: Used in packaging design, material fitting, mechanical engineering, and geometric modeling.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cubes. Other polyhedra have different insphere radius formulas.

Q5: What is the difference between insphere and circumsphere?
A: Insphere touches all faces from inside, while circumsphere touches all vertices from outside the cube.