1. What is Circumscribed Cylinder Radius of Cube?

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. This cylinder completely encloses the cube with the cube's vertices touching the cylinder's surface.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c(Cylinder) \) — Circumscribed Cylinder Radius of Cube (m)
• \( V \) — Volume of Cube (m³)

3. Formula Explanation

Derivation: The formula is derived from the relationship between the cube's volume and its spatial dimensions. The cube root of the volume gives the edge length of the cube, and the circumscribed cylinder radius is half the space diagonal of the cube divided by √2.

4. Using the Calculator

Instructions: Enter the volume of the cube in cubic meters. The volume must be a positive value greater than zero. The calculator will compute the radius of the circumscribed cylinder that contains the cube.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between cube volume and circumscribed cylinder radius?
A: The circumscribed cylinder radius is proportional to the cube root of the cube's volume, with a constant factor of 1/√2.

Q2: Can this formula be used for any cube?
A: Yes, this formula applies to all cubes regardless of size, as long as the volume is known.

Q3: What are the units of measurement?
A: The volume should be in cubic meters (m³) and the resulting radius will be in meters (m). Consistent units must be used throughout.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on geometric principles. The accuracy depends on the precision of the input volume value.

Q5: What is the significance of the √2 factor?
A: The √2 factor comes from the relationship between the cube's edge length and the diameter of its circumscribed cylinder, which is equal to the space diagonal of the cube.