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Insphere Radius of Cube given Circumscribed Cylinder Radius Calculator

Formula Used:

\[ r_i = \frac{r_{c(cylinder)}}{\sqrt{2}} \]

m

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1. What is the Insphere Radius of Cube?

The Insphere Radius of Cube is the radius of the sphere that is contained by the Cube in such a way that all the faces just touching the sphere. It represents the largest sphere that can fit inside a cube.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{r_{c(cylinder)}}{\sqrt{2}} \]

Where:

Explanation: This formula establishes the relationship between the insphere radius of a cube and the radius of its circumscribed cylinder.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and various engineering applications where sphere-cube relationships are relevant, such as in packaging, material science, and spatial analysis.

4. Using the Calculator

Tips: Enter the circumscribed cylinder radius of the cube in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumscribed cylinder of a cube?
A: A circumscribed cylinder of a cube is a cylinder that contains the cube such that all the vertices of the cube are touching the cylinder.

Q2: How is the insphere radius related to the cube's side length?
A: The insphere radius of a cube is equal to half of its side length.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cubes and their relationship with circumscribed cylinders.

Q4: What are practical applications of this calculation?
A: This calculation is useful in manufacturing, 3D modeling, and geometric design where precise spatial relationships between cubes and spheres are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though practical measurements may have some degree of error depending on the precision of input values.

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