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

Formula Used:

\[ TSA = \pi \times r \times \left( \frac{2 \times V}{\pi \times r^2} + r + \frac{d_{Space}}{2} \right) \]

Radius of Diagonally Halved Cylinder:

Volume of Diagonally Halved Cylinder:

m³

Space Diagonal of Diagonally Halved Cylinder:

Total Surface Area of Diagonally Halved Cylinder:

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

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \pi \times r \times \left( \frac{2 \times V}{\pi \times r^2} + r + \frac{d_{Space}}{2} \right) \]

Where:

\( TSA \) — Total Surface Area (m²)
\( r \) — Radius of Diagonally Halved Cylinder (m)
\( V \) — Volume of Diagonally Halved Cylinder (m³)
\( d_{Space} \) — Space Diagonal of Diagonally Halved Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the total surface area by considering the geometric properties of a cylinder that has been cut diagonally, incorporating the volume and space diagonal measurements.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for various engineering and manufacturing applications, including material estimation, heat transfer calculations, and structural analysis of diagonally halved cylindrical components.

4. Using the Calculator

Tips: Enter the radius in meters, volume in cubic 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 along a diagonal plane, resulting in two pieces with elliptical cross-sections instead of circular ones.

Q2: Why is the space diagonal important in this calculation?
A: The space diagonal helps determine the geometry of the elliptical face created by the diagonal cut, which is essential for accurate surface area calculation.

Q3: Can this formula be used for any diagonally cut cylinder?
A: Yes, this formula is specifically designed for cylinders that have been cut diagonally and uses the volume and space diagonal parameters to compute the surface area.

Q4: What units should I use for input values?
A: The calculator uses meters for length measurements and cubic meters for volume. Ensure consistent units for accurate results.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy of the result depends on the precision of your input measurements.