Long Height of Cut Cylinder given Lateral Surface Area Calculator

Long Height of Cut Cylinder Formula:

\[ h_{Long} = \frac{LSA}{\pi \times r} - h_{Short} \]

Long Height of Cut Cylinder (m):

1. What is Long Height of Cut Cylinder?

Definition: Long Height of Cut Cylinder is the longest vertical distance from the bottom circular face to the top elliptical face of the Cut Cylinder.

Purpose: This calculation helps in determining the dimensions of a cut cylinder when the lateral surface area and other parameters are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{Long} = \frac{LSA}{\pi \times r} - h_{Short} \]

Where:

\( h_{Long} \) — Long Height of Cut Cylinder (meters)
\( LSA \) — Lateral Surface Area (square meters)
\( r \) — Radius of Cut Cylinder (meters)
\( h_{Short} \) — Short Height of Cut Cylinder (meters)

Explanation: The formula calculates the long height by first determining the average height from the lateral surface area and radius, then subtracting the short height.

3. Importance of Long Height Calculation

Details: Accurate calculation of the long height is essential for engineering and construction applications involving cut cylinders, ensuring proper fit and structural integrity.

4. Using the Calculator

Tips: Enter the lateral surface area (m²), radius (m), and short height (m). All values must be positive numbers. The ±5% indicates the typical measurement tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between long height and short height?
A: The long height is the maximum vertical distance, while the short height is the minimum vertical distance from the base to the top of the cut cylinder.

Q2: Why is there a ±5% tolerance?
A: The tolerance accounts for measurement uncertainties and practical variations in real-world applications.

Q3: Can the short height be zero?
A: No, the short height must be greater than zero for a proper cut cylinder. If zero, it would be a regular cylinder.

Q4: What units should I use?
A: The calculator uses meters for all length measurements and square meters for area. Convert your measurements accordingly.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise, but real-world accuracy depends on the precision of your input measurements.