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The Circumsphere Radius of a Cube is the radius of the sphere that contains the Cube in such a way that all the vertices of the Cube are touching the sphere. It represents the smallest sphere that can completely enclose the cube.
The calculator uses the formula:
Where:
Explanation: The formula establishes a mathematical relationship between the circumsphere radius and midsphere radius of a cube, where the circumsphere radius is equal to the square root of 3/2 multiplied by the midsphere radius.
Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and spatial analysis. It helps determine the minimum spherical space required to contain a cube, which has applications in packaging, container design, and computational geometry.
Tips: Enter the midsphere radius of the cube in meters. The value must be positive and valid. The calculator will compute the corresponding circumsphere radius using the mathematical relationship between these two geometric properties.
Q1: What is the difference between circumsphere and midsphere?
A: The circumsphere touches all vertices of the cube, while the midsphere touches the midpoints of all edges of the cube.
Q2: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to cubes. Other polyhedrons have different relationships between their circumsphere and midsphere radii.
Q3: What are practical applications of this calculation?
A: This calculation is used in 3D modeling, game development, architectural design, and any field requiring spatial optimization of cubic objects within spherical containers.
Q4: How accurate is this formula?
A: The formula is mathematically exact for perfect cubes and provides precise results when accurate input values are provided.
Q5: What units should be used for the calculation?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.) as long as both input and output use the same units.