1. What is Volume of Cube given Circumscribed Cylinder Radius?

The volume of a cube can be calculated when the radius of its circumscribed cylinder is known. A circumscribed cylinder is one that completely encloses the cube, with all vertices of the cube touching the cylinder's surface.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of the cube (m³)
• \( r_c \) — Radius of the circumscribed cylinder (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula derives from the geometric relationship between a cube and its circumscribed cylinder, where the cylinder's diameter equals the space diagonal of the cube.

3. Importance of Volume Calculation

Details: Calculating volume from circumscribed cylinder radius is useful in engineering, architecture, and manufacturing where cylindrical constraints are given but cubic volume needs to be determined.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a circumscribed cylinder?
A: A circumscribed cylinder is a cylinder that completely encloses a cube, with all vertices of the cube touching the cylinder's surface.

Q2: How is the formula derived?
A: The formula comes from the relationship between the cube's space diagonal and the cylinder's diameter, where the space diagonal equals the cylinder's diameter.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.

Q4: What if I have the inscribed cylinder radius instead?
A: The formula would be different. This calculator specifically uses the circumscribed cylinder radius.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming perfect geometric shapes and precise input measurements.