Total Surface Area Of Flat End Cylinder Given Lateral Surface Area And Side Length Calculator

Formula Used:

\[ TSA = LSA + \pi \times l_{Side} \times \sqrt{l_{Side}^2 - h^2} + \pi \times (l_{Side}^2 - h^2) \]

Total Surface Area (TSA):

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1. What is the Total Surface Area of Flat End Cylinder?

The Total Surface Area of a Flat End Cylinder is the total quantity of plane enclosed on the entire surface of the Flat End Cylinder, including both the lateral surface area and the areas of the two flat ends.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = LSA + \pi \times l_{Side} \times \sqrt{l_{Side}^2 - h^2} + \pi \times (l_{Side}^2 - h^2) \]

Where:

\( TSA \) — Total Surface Area (m²)
\( LSA \) — Lateral Surface Area (m²)
\( l_{Side} \) — Side Length of Flat End Cylinder (m)
\( h \) — Height of Flat End Cylinder (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula calculates the total surface area by adding the lateral surface area to the areas of the two elliptical ends of the cylinder.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for various engineering and manufacturing applications, including material estimation, heat transfer calculations, and structural design of cylindrical components with flat ends.

4. Using the Calculator

Tips: Enter lateral surface area in m², side length in m, and height in m. All values must be positive, and side length must be greater than height for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Flat End Cylinder?
A: A Flat End Cylinder is a cylindrical shape with elliptical flat ends instead of circular ones, created by cutting a cylinder at an angle.

Q2: Why is the side length greater than height?
A: The side length represents the diagonal measurement of the elliptical end, which must be greater than the height to form a valid geometric shape.

Q3: Can this formula be used for circular cylinders?
A: No, this formula is specifically for flat end (oblique cut) cylinders. For regular circular cylinders, different formulas apply.

Q4: What units should be used?
A: Consistent units must be used (preferably meters for length and square meters for area). The calculator assumes metric units.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical formulas and provides results accurate to 6 decimal places for most practical applications.