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The Circumscribed Cylinder Radius of Cube is the radius of the cylinder that contains the Cube in such a way that all the vertices of the Cube are touching the cylinder. It represents the minimum radius required for a cylinder to perfectly enclose a cube.
The calculator uses the formula:
Where:
Explanation: The formula demonstrates the geometric relationship between the insphere radius of a cube and the radius of the smallest cylinder that can circumscribe it.
Details: This calculation is important in various engineering and design applications where cubes need to be fitted into cylindrical containers or housings, such as in mechanical engineering, packaging design, and architectural planning.
Tips: Enter the insphere radius of the cube in meters. The value must be positive and greater than zero. The calculator will automatically compute the circumscribed cylinder radius.
Q1: What is the relationship between cube side length and circumscribed cylinder radius?
A: The circumscribed cylinder radius equals half the space diagonal of the cube, which is \( \frac{\sqrt{3}}{2} \times \text{side length} \).
Q2: Can this formula be used for rectangular prisms?
A: No, this specific formula applies only to perfect cubes where all sides are equal.
Q3: What are typical applications of this calculation?
A: Used in mechanical engineering for fitting cubic components into cylindrical housings, in packaging design, and in various manufacturing processes.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cubes and provides precise results based on the input values.
Q5: What units should be used for the input?
A: The calculator accepts any consistent unit system, but meters are recommended for SI units. The result will be in the same units as the input.