Total Surface Area of Diagonally Halved Cylinder given Lateral Surface Area and Radius Calculator

Formula Used:

\[ TSA = \pi \times r \times \left( \frac{LSA}{\pi \times r} + r + \frac{dSpace}{2} \right) \]

Total Surface Area (TSA):

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1. What is Total Surface Area of Diagonally Halved Cylinder?

The Total Surface Area of a Diagonally Halved Cylinder is the total quantity of plane enclosed on the entire surface of the Diagonally Halved Cylinder, including both the curved lateral surface and the two elliptical bases formed by the diagonal cut.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \pi \times r \times \left( \frac{LSA}{\pi \times r} + r + \frac{dSpace}{2} \right) \]

Where:

\( TSA \) — Total Surface Area (m²)
\( r \) — Radius of Diagonally Halved Cylinder (m)
\( LSA \) — Lateral Surface Area (m²)
\( dSpace \) — Space Diagonal (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the total surface area by combining the lateral surface area with the areas of the two elliptical bases formed by the diagonal cut through 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 diagonally halved cylindrical components.

4. Using the Calculator

Tips: Enter the radius in meters, lateral surface area in square meters, and space diagonal in meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a diagonally halved cylinder?
A: A diagonally halved cylinder is a cylinder that has been cut diagonally across its length, resulting in two identical pieces with elliptical bases.

Q2: How is this different from a regular cylinder's surface area?
A: Unlike a regular cylinder with circular bases, a diagonally halved cylinder has elliptical bases, making the surface area calculation more complex.

Q3: What units should I use for input values?
A: Use consistent units (preferably meters for length and square meters for area) to ensure accurate results.

Q4: Can this formula be used for any diagonal cut?
A: This specific formula is designed for cylinders cut exactly diagonally through the center, creating two identical halves.

Q5: What if my cylinder has different dimensions?
A: This calculator is specifically designed for diagonally halved cylinders. For other cylinder configurations, different formulas would be required.