Radius of Flat End Cylinder given Volume Calculator

Formula Used:

\[ r = \sqrt{\frac{V}{h \times (\pi - \frac{4}{3})}} \]

Radius of Flat End Cylinder:

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1. What is the Radius of Flat End Cylinder Formula?

The formula calculates the radius of a flat end cylinder given its volume and height. This is derived from the volume formula of a flat end cylinder, solving for the radius.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \sqrt{\frac{V}{h \times (\pi - \frac{4}{3})}} \]

Where:

\( r \) — Radius of Flat End Cylinder (m)
\( V \) — Volume of Flat End Cylinder (m³)
\( h \) — Height of Flat End Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula rearranges the volume equation to solve for radius, using square root to isolate the radius variable.

3. Importance of Radius Calculation

Details: Calculating the radius is essential for various engineering and design applications involving flat end cylinders, including manufacturing, structural design, and volume optimization.

4. Using the Calculator

Tips: Enter volume in cubic meters (m³), height in meters (m). All values must be valid positive numbers. The calculator will compute the radius in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a flat end cylinder?
A: A flat end cylinder is a cylindrical shape with flat, circular ends rather than rounded or hemispherical ends.

Q2: Why is there a (π - 4/3) term in the formula?
A: This term comes from the specific geometry of flat end cylinders and represents the mathematical relationship between volume, height, and radius for this shape.

Q3: What units should I use for input values?
A: The calculator uses meters for length units and cubic meters for volume. Convert your measurements accordingly before calculation.

Q4: Can this formula be used for any cylinder?
A: No, this specific formula applies only to flat end cylinders. Other cylinder types (like those with hemispherical ends) have different volume formulas.

Q5: What if I get an error message?
A: This typically means the input values result in an invalid mathematical operation (like division by zero or square root of a negative number). Check that both volume and height are positive values.