1. What is the Volume of Cube given Circumsphere Radius?

The volume of a cube can be calculated using the circumsphere radius, which is the radius of the sphere that contains the cube such that all vertices of the cube touch the sphere. This provides an alternative method to calculate cube volume when the circumsphere radius is known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Cube (m³)
• \( r_c \) — Circumsphere Radius of Cube (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula derives from the relationship between the cube's side length and its circumsphere radius, converted to volume calculation.

3. Importance of Volume Calculation

Details: Calculating volume from circumsphere radius is useful in geometry problems, 3D modeling, and engineering applications where the circumsphere measurement might be more readily available than direct side measurements.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding volume of the cube.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between cube side length and circumsphere radius?
A: The circumsphere radius \( r_c \) relates to the side length \( a \) as \( r_c = \frac{a\sqrt{3}}{2} \).

Q2: Can this formula be used for any cube?
A: Yes, this formula applies to all perfect cubes regardless of size, as it's derived from geometric principles.

Q3: What are the units for the result?
A: The volume is calculated in cubic meters (m³), matching the input unit of circumsphere radius.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, though practical accuracy depends on the precision of the input measurement.

Q5: Can I calculate circumsphere radius from volume using this formula?
A: Yes, the formula can be rearranged to solve for circumsphere radius given the volume: \( r_c = \frac{\sqrt{3}}{2} \times \sqrt[3]{V} \).