Total Surface Area of Cut Cylinder given Lateral Surface Area Calculator

Total Surface Area Formula:

\[ TSA = \pi \times r \times (r + b + \frac{LSA}{\pi \times r}) \]

Radius of Cut Cylinder:

Semi Minor Axis:

Lateral Surface Area:

m²

Tolerance:

Total Surface Area (m²):

±5% Range (m²):

1. What is Total Surface Area of Cut Cylinder?

Definition: The total surface area of a cut cylinder includes the area of both circular bases, the elliptic face, and the lateral surface.

Purpose: This calculation is essential in engineering and construction for determining material requirements for cylindrical structures with non-parallel cuts.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \pi \times r \times (r + b + \frac{LSA}{\pi \times r}) \]

Where:

\( TSA \) — Total Surface Area (m²)
\( r \) — Radius of the cylinder (m)
\( b \) — Semi-minor axis of the elliptic face (m)
\( LSA \) — Lateral Surface Area (m²)

3. Importance of Tolerance

Details: The ±5% tolerance accounts for measurement errors, material variations, and construction imperfections. Adjust as needed for your project requirements.

4. Using the Calculator

Tips:

Enter all dimensions in meters
Lateral surface area should include the curved side area
Adjust tolerance percentage as needed (default ±5%)

5. Frequently Asked Questions (FAQ)

Q1: What's a typical tolerance for construction projects?
A: ±5% is common, but critical projects may require tighter tolerances (±2-3%).

Q2: How do I measure the semi-minor axis?
A: It's half the length of the shortest diameter across the elliptic face.

Q3: Does this include both circular bases?
A: Yes, the formula accounts for all surfaces including both circular ends.

Q4: What if my cylinder has different radii?
A: This calculator assumes a uniform radius. For tapered cylinders, use specialized formulas.

Q5: How precise should my measurements be?
A: Measure to the highest precision possible, especially for small cylinders.