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Circumsphere Radius Of Cube Given Circumscribed Cylinder Radius Calculator

Formula Used:

\[ \text{Circumsphere Radius of Cube} = \sqrt{\frac{3}{2}} \times \text{Circumscribed Cylinder Radius of Cube} \]

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1. What is Circumsphere Radius of Cube?

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.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Circumsphere Radius of Cube} = \sqrt{\frac{3}{2}} \times \text{Circumscribed Cylinder Radius of Cube} \]

Where:

Explanation: This formula establishes the relationship between the circumsphere radius and the circumscribed cylinder radius of a cube through geometric principles.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in various geometric applications, 3D modeling, packaging design, and spatial analysis where understanding the minimal spherical enclosure of a cube is required.

4. Using the Calculator

Tips: Enter the circumscribed cylinder radius of the cube in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between circumsphere and circumscribed cylinder?
A: The circumsphere is the smallest sphere that contains the cube, while the circumscribed cylinder is the smallest cylinder that contains the cube with all vertices touching the cylinder surface.

Q2: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cubes. Other polyhedra have different relationships between their circumsphere and circumscribed cylinder radii.

Q3: What are practical applications of this calculation?
A: This calculation is used in packaging design, 3D modeling, architectural planning, and any field requiring optimal spatial arrangement of cubic objects.

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 as the default unit, but any consistent unit of length can be used as long as both input and output use the same unit system.

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