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The edge length of a cube given its circumscribed cylinder radius is the length of any edge of the cube when the radius of the cylinder that circumscribes the cube is known. A circumscribed cylinder is one that contains the cube such that all vertices of the cube touch the cylinder.
The calculator uses the formula:
Where:
Explanation: The relationship between the cube's edge length and the circumscribed cylinder radius is derived from the geometric properties of a cube inscribed in a cylinder.
Details: Calculating the edge length from the circumscribed cylinder radius is important in geometry, engineering, and design applications where cubes and cylinders interact. It helps in determining spatial relationships and dimensions in 3D modeling.
Tips: Enter the circumscribed cylinder radius in meters. The value must be positive and valid. The calculator will compute the corresponding edge length of the cube.
Q1: What is a circumscribed cylinder?
A: A circumscribed cylinder is a cylinder that contains a given solid (in this case, a cube) such that all vertices of the solid touch the inner surface of the cylinder.
Q2: Why is the square root of 2 used in this formula?
A: The square root of 2 appears because the relationship between the cube's edge length and the cylinder's radius involves the diagonal of the cube's face, which is \( edge \times \sqrt{2} \).
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cubes. Other polyhedra have different relationships between their dimensions and circumscribed cylinder radii.
Q4: What are the units for the inputs and outputs?
A: The calculator uses meters for both input (cylinder radius) and output (edge length), but any consistent unit system can be used as long as the same unit is maintained throughout.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact, based on geometric principles. The accuracy of the result depends on the precision of the input value provided.