Volume of Hollow Cylinder Given Total Surface Area Calculator

Formula Used:

\[ V = \pi \times \left( \frac{TSA}{2\pi (r_{Inner} + r_{Outer})} - r_{Outer} + r_{Inner} \right) \times (r_{Outer}^2 - r_{Inner}^2) \]

Volume of Hollow Cylinder (V):

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1. What is the Volume of Hollow Cylinder?

The Volume of Hollow Cylinder is the total quantity of three dimensional space enclosed by the entire surface of the Hollow Cylinder. It represents the capacity or the amount of material that can be contained within the hollow cylindrical structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \pi \times \left( \frac{TSA}{2\pi (r_{Inner} + r_{Outer})} - r_{Outer} + r_{Inner} \right) \times (r_{Outer}^2 - r_{Inner}^2) \]

Where:

\( V \) — Volume of Hollow Cylinder (m³)
\( TSA \) — Total Surface Area of Hollow Cylinder (m²)
\( r_{Inner} \) — Inner Radius of Hollow Cylinder (m)
\( r_{Outer} \) — Outer Radius of Hollow Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the volume of a hollow cylinder based on its total surface area and both inner and outer radii, taking into account the cylindrical geometry and the hollow nature of the structure.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining material requirements, capacity planning, structural analysis, and various engineering applications involving hollow cylindrical components.

4. Using the Calculator

Tips: Enter total surface area in square meters, inner and outer radii in meters. All values must be positive, and outer radius must be greater than inner radius for a valid hollow cylinder.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow cylinder?
A: A hollow cylinder is a three-dimensional geometric shape that consists of two concentric cylinders, where the inner cylinder is removed from the outer one, creating a hollow space.

Q2: How is this different from a solid cylinder volume?
A: For a solid cylinder, volume is simply πr²h. For a hollow cylinder, you subtract the volume of the inner hollow space from the volume of the outer cylinder.

Q3: What are common applications of hollow cylinders?
A: Hollow cylinders are used in pipes, tubes, storage tanks, structural columns, and various mechanical components where strength-to-weight ratio is important.

Q4: What units should I use for input?
A: The calculator uses meters for length units and square meters for area units. You can convert from other units as needed before input.

Q5: Can this formula be used for any hollow cylinder?
A: This formula applies to right circular hollow cylinders where the inner and outer surfaces are concentric and parallel.