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

The volume of a cube given the inscribed cylinder radius refers to the total three-dimensional space enclosed by a cube, calculated using the radius of the largest cylinder that can fit perfectly inside the cube, touching all its faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of the cube (m³)
• \( r_i(Cylinder) \) — Radius of the inscribed cylinder (m)

Explanation: The diameter of the inscribed cylinder equals the side length of the cube, so the side length is twice the cylinder radius. The volume is then the cube of this side length.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in determining capacity, material requirements, and spatial relationships.

4. Using the Calculator

Tips: Enter the inscribed cylinder 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 an inscribed cylinder in a cube?
A: An inscribed cylinder in a cube is the largest cylinder that can fit inside the cube, with its curved surface touching all six faces of the cube.

Q2: How is the cylinder radius related to the cube's side length?
A: The diameter of the inscribed cylinder equals the side length of the cube, meaning the side length is exactly twice the cylinder radius.

Q3: What are the units for volume calculation?
A: The volume is calculated in cubic meters (m³) when using meters for radius input. Ensure consistent units for accurate results.

Q4: Can this formula be used for any cube?
A: Yes, this formula applies to all perfect cubes where a cylinder is inscribed such that it touches all faces.

Q5: What if I have the cylinder diameter instead of radius?
A: Simply divide the diameter by 2 to get the radius, then use the calculator with that radius value.