1. What is the Radius of Half Cylinder given Space Diagonal?

The radius of a half cylinder can be determined using the space diagonal and height through the Pythagorean theorem. This calculation is essential in geometry for understanding the dimensions of half cylindrical objects.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of Half Cylinder (m)
• \( d_{Space} \) — Space Diagonal of Half Cylinder (m)
• \( h \) — Height of Half Cylinder (m)

Explanation: The formula derives from the Pythagorean theorem applied to the right triangle formed by the space diagonal, height, and radius.

3. Importance of Radius Calculation

Details: Calculating the radius accurately is crucial for determining the volume, surface area, and other geometric properties of half cylindrical structures in engineering and architecture.

4. Using the Calculator

Tips: Enter the space diagonal and height in meters. Ensure both values are positive and the space diagonal is greater than the height for a valid result.

5. Frequently Asked Questions (FAQ)

Q1: Why must the space diagonal be greater than the height?
A: Since the radius is calculated using the square root of the difference of squares, the space diagonal must be larger than the height to avoid negative values under the square root.

Q2: What units should be used?
A: The calculator uses meters (m) by default, but any consistent unit of length can be used as long as both inputs are in the same unit.

Q3: Can this formula be used for full cylinders?
A: Yes, the same principle applies to full cylinders when calculating the radius from the space diagonal and height.

Q4: What if the inputs result in a negative under the square root?
A: The calculator will display an error, indicating that the space diagonal must be greater than the height.

Q5: How precise is the calculation?
A: The result is rounded to four decimal places for practicality, but the underlying calculation uses precise arithmetic.