1. What is the Insphere Radius of Cube?

The Insphere Radius of Cube is the radius of the sphere that is contained by the Cube in such a way that all the faces just touching the sphere. It represents the largest sphere that can fit inside the cube.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius of Cube (m)
• \( A_{Face} \) — Face Area of Cube (m²)

Explanation: The formula calculates the insphere radius by taking the square root of the face area and dividing it by 2. This relationship exists because the face area of a cube is equal to the square of its side length, and the insphere radius is half the side length.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and engineering applications where understanding the maximum size of a sphere that can fit inside a cube is necessary for design, packaging, or spatial analysis purposes.

4. Using the Calculator

Tips: Enter the face area of the cube in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between face area and side length of a cube?
A: The face area of a cube is equal to the square of its side length (A = s²).

Q2: How is the insphere radius related to the side length?
A: The insphere radius is exactly half of the side length of the cube (r_i = s/2).

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cubes. Other polyhedra have different relationships between face area and insphere radius.

Q4: What are the units for the insphere radius?
A: The insphere radius will have the same units as the square root of the face area. If face area is in m², the radius will be in meters.

Q5: Is the insphere always tangent to all faces of the cube?
A: Yes, by definition, the insphere is tangent to all six faces of the cube.