Total Surface Area Of Diagonally Halved Cylinder Given Volume And Height Calculator

Formula Used:

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

Volume Of Diagonally Halved Cylinder (V):

m³

Height Of Diagonally Halved Cylinder (h):

Space Diagonal Of Diagonally Halved Cylinder (d_Space):

Total Surface Area Of Diagonally Halved Cylinder (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is The Total Surface Area Of Diagonally Halved Cylinder Given Volume And Height?

The Total Surface Area of a Diagonally Halved Cylinder refers to the complete area covering all surfaces of the cylinder after it has been cut diagonally. This includes the curved surface area and the areas of the two elliptical faces created by the diagonal cut.

2. How Does The Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the total surface area by considering the geometric properties of a diagonally halved cylinder, incorporating volume, height, and space diagonal measurements.

3. Importance Of Total Surface Area Calculation

Details: Calculating the total surface area is essential for various engineering and architectural applications, including material estimation, heat transfer calculations, and structural analysis of cylindrical components that have been diagonally sectioned.

4. Using The Calculator

Tips: Enter the volume in cubic meters (m³), height in meters (m), and space diagonal in meters (m). 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.

Q2: Why is the space diagonal important in this calculation?
A: The space diagonal represents the longest distance across the elliptical face and is crucial for accurately calculating the surface area of the diagonally cut surfaces.

Q3: Can this formula be used for partially filled cylindrical tanks?
A: Yes, this formula can be adapted for calculating the wetted surface area in partially filled cylindrical tanks that are diagonally oriented.

Q4: What are the units for the calculated surface area?
A: The surface area is calculated in square meters (m²), but can be converted to other area units as needed.

Q5: How accurate is this calculation for real-world applications?
A: The formula provides theoretical accuracy. For practical applications, factors like material thickness, surface roughness, and manufacturing tolerances should be considered.