Total Surface Area Of Cut Cylinder Given Lateral Surface Area And Heights Calculator

Formula Used:

\[ TSA = \frac{LSA}{h_{Long} + h_{Short}} \times \left( \frac{LSA}{\pi \times (h_{Long} + h_{Short})} + b + h_{Long} + h_{Short} \right) \]

Lateral Surface Area of Cut Cylinder (LSA):

m²

Long Height of Cut Cylinder (hLong):

Short Height of Cut Cylinder (hShort):

Semi Minor Axis of Cut Cylinder (b):

Total Surface Area of Cut Cylinder (TSA):

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1. What is the Total Surface Area of Cut Cylinder Formula?

The Total Surface Area of a Cut Cylinder is calculated using a specific formula that takes into account the lateral surface area, both heights (long and short), and the semi-minor axis of the elliptic face. This provides a comprehensive measurement of all surfaces of the cut cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{LSA}{h_{Long} + h_{Short}} \times \left( \frac{LSA}{\pi \times (h_{Long} + h_{Short})} + b + h_{Long} + h_{Short} \right) \]

Where:

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

Explanation: The formula calculates the total surface area by considering the lateral surface area, the sum of heights, and the semi-minor axis to account for all surfaces of the cut cylinder.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various engineering and architectural applications, including material estimation, heat transfer calculations, and structural analysis of cylindrical components with elliptical cuts.

4. Using the Calculator

Tips: Enter all values in meters (m) and square meters (m²). Ensure all values are positive and valid (LSA > 0, heights > 0, semi-minor axis ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a cut cylinder?
A: A cut cylinder is a cylindrical shape that has been sliced at an angle, resulting in an elliptical top face instead of a circular one.

Q2: Why are there two different heights?
A: The long and short heights represent the maximum and minimum vertical distances from the base to the elliptical top face due to the angled cut.

Q3: What is the semi-minor axis?
A: The semi-minor axis is half the length of the shortest diameter of the elliptical top face of the cut cylinder.

Q4: Can this formula be used for any cut angle?
A: Yes, the formula is general and works for any cut angle, as the parameters account for the resulting geometry.

Q5: What units should I use?
A: Use consistent units (preferably meters for length and square meters for area) for accurate results.