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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 a cube.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the midsphere radius and the insphere radius of a cube, where the insphere radius is exactly \( \frac{1}{\sqrt{2}} \) times the midsphere radius.
Details: Calculating the insphere radius is important in geometry and various engineering applications where understanding the spatial relationships within a cube is necessary, such as in packaging design, material science, and architectural planning.
Tips: Enter the midsphere radius of the cube in meters. The value must be positive and valid. The calculator will compute the corresponding insphere radius using the mathematical relationship between these two geometric properties.
Q1: What is the difference between insphere radius and midsphere radius?
A: The insphere radius is the radius of the sphere that touches all faces of the cube, while the midsphere radius is the radius of the sphere that touches all edges of the cube.
Q2: Why is there a square root of 2 in the formula?
A: The square root of 2 appears due to the geometric relationship between the face diagonals and edges of a cube, which follows from the Pythagorean theorem.
Q3: Can this formula be used for any cube?
A: Yes, this formula applies to all perfect cubes regardless of size, as it describes the constant mathematical relationship between these two geometric properties.
Q4: What are typical values for insphere radius?
A: The insphere radius is always half the edge length of the cube. For a cube with edge length a, the insphere radius is a/2.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cubes. The accuracy depends only on the precision of the input value and the computational precision of the calculator.