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Circumsphere Radius of 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 distance from the center of the cube to any of its vertices.
The calculator uses the formula:
Where:
Explanation: The circumsphere radius is exactly half the length of the space diagonal of the cube, as the space diagonal passes through the center of the circumsphere and connects two opposite vertices.
Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and various engineering applications where understanding the spatial relationships and bounding spheres of cubic objects is necessary.
Tips: Enter the space diagonal of the cube in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is the relationship between circumsphere radius and cube side length?
A: The circumsphere radius can also be calculated as \( r_c = \frac{\sqrt{3}}{2} \times a \), where a is the side length of the cube.
Q2: How is circumsphere radius different from insphere radius?
A: Circumsphere radius touches all vertices of the cube, while insphere radius touches the center of all faces (inscribed sphere).
Q3: Can this formula be used for other rectangular prisms?
A: No, this specific formula applies only to perfect cubes where all sides are equal. For rectangular prisms, the circumsphere radius calculation is more complex.
Q4: What are practical applications of circumsphere radius?
A: Used in computer graphics for bounding spheres, collision detection, and in packaging design to determine minimum spherical container size.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cubes. The accuracy depends on the precision of the input space diagonal measurement.