1. What is Circumscribed Cylinder Radius of Cube?

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.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumscribed Cylinder Radius of Cube (m)
• \( r_i \) — Inscribed Cylinder Radius of Cube (m)

Explanation: This formula demonstrates the mathematical relationship between the circumscribed and inscribed cylinder radii of a cube, where the circumscribed radius is exactly √2 times the inscribed radius.

3. Importance of Circumscribed Cylinder Radius Calculation

Details: Calculating the circumscribed cylinder radius is important in geometric modeling, engineering design, and understanding spatial relationships between different geometric shapes.

4. Using the Calculator

Tips: Enter the inscribed cylinder radius in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between circumscribed and inscribed cylinders?
A: A circumscribed cylinder contains the cube with all vertices touching the cylinder, while an inscribed cylinder is contained within the cube with all faces touching the cylinder.

Q2: Why is the constant √2 used in this formula?
A: The √2 factor comes from the geometric relationship between the cube's spatial dimensions and the Pythagorean theorem applied to the cube's diagonal cross-section.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to cubes due to their unique symmetrical properties.

Q4: What are practical applications of this calculation?
A: This calculation is used in mechanical engineering, architecture, 3D modeling, and packaging design where cylindrical containers need to accommodate cubic objects.

Q5: How accurate is this formula?
A: The formula is mathematically exact and provides perfect accuracy for ideal geometric cubes.