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The Inscribed Cylinder Radius of Cube is the radius of the cylinder that is contained by the Cube in such a way that all the faces of the Cube are just touching the cylinder. This represents the largest possible cylinder that can fit inside a cube.
The calculator uses the formula:
Where:
Explanation: The radius of the largest cylinder that can be inscribed in a cube is exactly half the edge length of the cube, as the cylinder's diameter equals the cube's edge length.
Details: This calculation is important in geometry, engineering, and manufacturing where cylindrical objects need to be fitted inside cubic containers or spaces with maximum efficiency.
Tips: Enter the edge length of the cube in meters. The value must be positive and greater than zero.
Q1: Why is the inscribed cylinder radius half the cube's edge length?
A: Because the cylinder's diameter must equal the cube's edge length to fit perfectly inside, making the radius exactly half of that length.
Q2: Does this work for all cube sizes?
A: Yes, this relationship holds true for cubes of any size, as it's based on geometric proportions rather than absolute measurements.
Q3: What is the volume of the inscribed cylinder?
A: The volume can be calculated using \( V = \pi r^2 h = \pi (\frac{l_e}{2})^2 l_e = \frac{\pi}{4} l_e^3 \), where height equals the cube's edge length.
Q4: Can this formula be used for rectangular prisms?
A: No, this specific formula only applies to perfect cubes. For rectangular prisms, the calculation depends on which dimension is the limiting factor.
Q5: What are practical applications of this calculation?
A: This is used in packaging design, mechanical engineering, architecture, and manufacturing where cylindrical objects need to be optimally placed within cubic spaces.