Radius of Cut Cylinder given Volume Calculator

Formula Used:

\[ r = \sqrt{\frac{V}{\pi \times \frac{h_{Short} + h_{Long}}{2}}} \]

Radius of Cut Cylinder:

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1. What is the Radius of Cut Cylinder Formula?

The formula calculates the radius of a cut cylinder given its volume and the short and long heights. This is particularly useful in engineering and geometry applications where you need to determine the base radius of a truncated cylindrical object.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \sqrt{\frac{V}{\pi \times \frac{h_{Short} + h_{Long}}{2}}} \]

Where:

\( r \) — Radius of Cut Cylinder (m)
\( V \) — Volume of Cut Cylinder (m³)
\( h_{Short} \) — Short Height of Cut Cylinder (m)
\( h_{Long} \) — Long Height of Cut Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the radius by taking the square root of the volume divided by π times the average of the short and long heights.

3. Importance of Radius Calculation

Details: Calculating the radius of a cut cylinder is essential in various engineering applications, including structural design, fluid dynamics, and manufacturing processes where cylindrical components are cut at an angle.

4. Using the Calculator

Tips: Enter the volume in cubic meters, and both short and long heights in meters. All values must be positive numbers. The calculator will compute the radius in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a cut cylinder?
A: A cut cylinder is a cylindrical object that has been sliced at an angle, resulting in two different heights at opposite ends of the elliptical cross-section.

Q2: Why use the average height in the formula?
A: The average height provides an effective height value that accounts for the slanted nature of the cut cylinder, allowing for accurate volume-to-radius conversion.

Q3: Can this formula be used for any cut angle?
A: Yes, this formula works for any cut angle as long as you have the correct short and long height measurements.

Q4: What units should I use?
A: The calculator uses meters for all linear measurements and cubic meters for volume. Ensure consistent units for accurate results.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The accuracy of the result depends on the precision of your input measurements.