Radius of Sharp Bent Cylinder given Volume Calculator

Formula Used:

\[ r = \sqrt{\frac{2V}{\pi(h_{1s} + h_{1l} + h_{2l} + h_{2s})}} \]

Volume of Sharp Bent Cylinder (V):

m³

First Short Height (h₁ₛ):

First Long Height (h₁ₗ):

Second Long Height (h₂ₗ):

Second Short Height (h₂ₛ):

Radius of Sharp Bent Cylinder (r):

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1. What is the Radius of Sharp Bent Cylinder Formula?

The formula calculates the radius of a sharp bent cylinder based on its volume and the four height measurements (first short, first long, second long, and second short heights). This geometric relationship helps determine the cylinder's base radius when other dimensional parameters are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \sqrt{\frac{2V}{\pi(h_{1s} + h_{1l} + h_{2l} + h_{2s})}} \]

Where:

\( r \) — Radius of Sharp Bent Cylinder (m)
\( V \) — Volume of Sharp Bent Cylinder (m³)
\( h_{1s} \) — First Short Height (m)
\( h_{1l} \) — First Long Height (m)
\( h_{2l} \) — Second Long Height (m)
\( h_{2s} \) — Second Short Height (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula derives from the geometric properties of the sharp bent cylinder, relating the volume to the radius through the sum of the four height measurements.

3. Importance of Radius Calculation

Details: Calculating the radius is essential for understanding the cylinder's dimensions, manufacturing precision, structural analysis, and various engineering applications where geometric accuracy is crucial.

4. Using the Calculator

Tips: Enter all values in meters. Ensure volume and all height values are positive numbers. The calculator will compute the radius based on the provided measurements.

5. Frequently Asked Questions (FAQ)

Q1: What is a sharp bent cylinder?
A: A sharp bent cylinder is a geometric shape formed by bending a cylinder at a sharp angle, creating distinct height measurements on different sides.

Q2: Why are four different height measurements needed?
A: The four heights represent the different vertical dimensions created by the sharp bending, which are necessary to accurately calculate the volume and subsequently the radius.

Q3: What units should I use for input?
A: The calculator uses meters for all measurements. Convert other units to meters before inputting values.

Q4: Can this formula be used for other cylinder types?
A: This specific formula is designed for sharp bent cylinders with the described geometric configuration and may not apply to other cylinder variations.

Q5: What if I get an error result?
A: An error typically occurs when the denominator becomes zero or negative. Ensure all height values are positive and their sum is greater than zero.