Short Height of Cut Cylinder given Total Surface Area Calculator

Formula Used:

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

Total Surface Area of Cut Cylinder (TSA):

m²

Radius of Cut Cylinder (r):

Semi Minor Axis of Cut Cylinder (b):

Long Height of Cut Cylinder (h_Long):

Short Height of Cut Cylinder (h_Short):

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1. What is Short Height of Cut Cylinder?

Short Height of Cut Cylinder is the shortest vertical distance from the bottom circular face to the top elliptical face of the Cut Cylinder. It represents the minimum height measurement of the truncated cylindrical shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h_{Short} \) — Short Height of Cut Cylinder (m)
\( TSA \) — Total Surface Area of Cut Cylinder (m²)
\( r \) — Radius of Cut Cylinder (m)
\( b \) — Semi Minor Axis of Cut Cylinder (m)
\( h_{Long} \) — Long Height of Cut Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the short height by rearranging the total surface area equation of a cut cylinder, accounting for all surface components including the circular base, elliptical top, and lateral surface.

3. Importance of Short Height Calculation

Details: Calculating the short height is essential for determining the complete geometry of cut cylinders, which is crucial in engineering design, architectural applications, and manufacturing processes where precise dimensional measurements are required.

4. Using the Calculator

Tips: Enter all values in meters. Total Surface Area and Radius must be positive values. Semi Minor Axis and Long Height must be non-negative values. Ensure consistent units for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cut Cylinder?
A: A Cut Cylinder is a cylindrical shape that has been truncated or cut by an inclined plane, resulting in an elliptical top surface instead of a circular one.

Q2: How is this different from a regular cylinder?
A: Unlike a regular cylinder with parallel circular bases, a cut cylinder has one circular base and one elliptical top surface due to the inclined cut.

Q3: What practical applications use cut cylinders?
A: Cut cylinders are used in various engineering applications including piping systems, architectural elements, mechanical components, and fluid storage tanks with slanted tops.

Q4: Can the short height be negative?
A: No, the short height represents a physical dimension and should always be a positive value. If the calculation yields a negative result, check your input values for accuracy.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of cut cylinders, provided accurate input values are used.