Total Surface Area of Cut Cylinder given Volume and Heights Calculator

Formula Used:

\[ TSA = \sqrt{\frac{2\pi V}{h_{Long}+h_{Short}}} \times \left( \sqrt{\frac{2V}{\pi(h_{Long}+h_{Short})}} + b + h_{Short} + h_{Long} \right) \]

Volume of Cut Cylinder (V):

m³

Long Height of Cut Cylinder (h_Long):

Short Height of Cut Cylinder (h_Short):

Semi Minor Axis of Cut Cylinder (b):

Total Surface Area of Cut Cylinder (TSA):

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1. What is the Total Surface Area of Cut Cylinder?

The Total Surface Area of a Cut Cylinder is the total quantity of plane enclosed on the entire surface of the Cut Cylinder, including both circular and elliptical faces as well as the lateral surface area.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \sqrt{\frac{2\pi V}{h_{Long}+h_{Short}}} \times \left( \sqrt{\frac{2V}{\pi(h_{Long}+h_{Short})}} + b + h_{Short} + h_{Long} \right) \]

Where:

\( TSA \) — Total Surface Area of Cut Cylinder (m²)
\( V \) — Volume of Cut Cylinder (m³)
\( h_{Long} \) — Long Height of Cut Cylinder (m)
\( h_{Short} \) — Short Height of Cut Cylinder (m)
\( b \) — Semi Minor Axis of Cut Cylinder (m)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: This formula calculates the total surface area based on the volume and geometric properties of the cut cylinder, accounting for both the elliptical top and circular bottom surfaces.

3. Importance of Total Surface Area Calculation

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

4. Using the Calculator

Tips: Enter all values in meters and cubic meters. Ensure all values are positive and valid. The long height must be greater than or equal to the short height for a physically meaningful result.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cut Cylinder?
A: A Cut Cylinder is a cylindrical shape that has been cut by a plane at an angle, resulting in an elliptical top surface while maintaining a circular bottom surface.

Q2: Why are there two different heights?
A: The cut creates a slanted top surface, resulting in varying heights from the bottom to different points on the top elliptical surface. The long and short heights represent the maximum and minimum vertical distances.

Q3: What is the Semi Minor Axis?
A: The Semi Minor Axis is half the length of the shortest diameter of the elliptical top surface of the cut cylinder.

Q4: Can this formula be used for any cut angle?
A: Yes, this formula is general and works for any cut angle, as the geometric properties (heights and semi-minor axis) capture the specific configuration of the cut.

Q5: What are typical applications of cut cylinders?
A: Cut cylinders are commonly found in engineering components such as pressure vessels with inclined openings, architectural elements, and various mechanical parts where cylindrical shapes intersect at angles.