Volume of Cut Cylinder given Total Surface Area Calculator

Formula Used:

\[ V = \frac{r}{2} \times (TSA - (\pi \times r \times (r + b))) \]

Radius of Cut Cylinder:

Total Surface Area of Cut Cylinder:

m²

Semi Minor Axis of Cut Cylinder:

Volume of Cut Cylinder:

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1. What is the Volume of Cut Cylinder?

The Volume of Cut Cylinder is the total quantity of three dimensional space enclosed by the entire surface of the Cut Cylinder. It represents the capacity or the amount of material that the cut cylinder can hold.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{r}{2} \times (TSA - (\pi \times r \times (r + b))) \]

Where:

\( V \) — Volume of Cut Cylinder (m³)
\( r \) — Radius of Cut Cylinder (m)
\( TSA \) — Total Surface Area of Cut Cylinder (m²)
\( b \) — Semi Minor Axis of Cut Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: This formula calculates the volume of a cut cylinder based on its radius, total surface area, and semi minor axis of the elliptic face.

3. Importance of Volume Calculation

Details: Calculating the volume of a cut cylinder is important in various engineering and architectural applications, particularly in determining material requirements, capacity planning, and structural design calculations.

4. Using the Calculator

Tips: Enter the radius in meters, total surface area in square meters, and semi minor axis in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a cut cylinder?
A: A cut cylinder is a cylindrical shape that has been sliced or cut at an angle, resulting in an elliptical cross-section rather than a circular one.

Q2: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy depends on the precision of the measurements provided.

Q3: Can this formula be used for any type of cylinder?
A: This specific formula is designed for cut cylinders with elliptical cross-sections. It may not be applicable to regular cylinders or cylinders with different types of cuts.

Q4: What are typical applications of cut cylinders?
A: Cut cylinders are commonly found in piping systems, architectural elements, mechanical components, and various industrial designs where angled connections are required.

Q5: How does the semi minor axis affect the volume?
A: The semi minor axis, along with the radius, determines the elliptical shape of the cut surface, which directly influences the volume calculation of the cut cylinder.