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Circumsphere Radius Formula:
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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 distance from the center of the cube to any of its vertices.
The calculator uses the formula:
Where:
Explanation: The formula derives from the relationship between the cube's lateral surface area and its spatial geometry, using the square root function to calculate the radius.
Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and engineering applications where understanding the spatial dimensions and containment of cubic structures is required.
Tips: Enter the lateral surface area of the cube in square meters. The value must be positive and valid (LSA > 0).
Q1: What is the difference between circumsphere radius and insphere radius?
A: Circumsphere radius touches all vertices of the cube, while insphere radius touches all faces from the inside (inscribed sphere).
Q2: How is lateral surface area different from total surface area?
A: Lateral surface area excludes the top and bottom faces, while total surface area includes all six faces of the cube.
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. Other rectangular prisms have different circumsphere radius calculations.
Q4: What are typical applications of circumsphere radius calculation?
A: Used in packaging design, 3D modeling, architectural planning, and any application requiring spherical containment of cubic objects.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cubes. Accuracy depends on the precision of the input lateral surface area measurement.