Height of Hollow Cylinder Given Total Surface Area Calculator

Formula Used:

\[ h = \frac{TSA}{2\pi(r_{inner} + r_{outer})} - r_{outer} + r_{inner} \]

Height of Hollow Cylinder (h):

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1. What is the Height of Hollow Cylinder Formula?

The height of a hollow cylinder can be calculated from its total surface area and inner/outer radii using the formula: \[ h = \frac{TSA}{2\pi(r_{inner} + r_{outer})} - r_{outer} + r_{inner} \] This formula is derived from the total surface area formula of a hollow cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{TSA}{2\pi(r_{inner} + r_{outer})} - r_{outer} + r_{inner} \]

Where:

\( h \) — Height of Hollow Cylinder (m)
\( TSA \) — Total Surface Area (m²)
\( r_{inner} \) — Inner Radius (m)
\( r_{outer} \) — Outer Radius (m)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: The formula rearranges the total surface area equation to solve for height, accounting for both the inner and outer curved surfaces plus the two annular bases.

3. Importance of Height Calculation

Details: Calculating the height of a hollow cylinder is essential in engineering, manufacturing, and architectural applications where precise dimensional calculations are required for material estimation, structural design, and volume capacity planning.

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 consisting of two concentric cylinders with the same height but different radii, creating a hollow space inside.

Q2: Why is the outer radius always greater than the inner radius?
A: For a hollow cylinder to exist, the outer radius must be greater than the inner radius. If they are equal, it becomes a solid cylinder with no hollow space.

Q3: Can this formula be used for imperial units?
A: Yes, but all measurements must use consistent units (e.g., all in inches or all in feet for both radii and surface area).

Q4: What if I get a negative height result?
A: A negative height indicates invalid input values. Check that the surface area is sufficient for the given radii and that outer radius > inner radius.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The practical accuracy depends on the precision of your measurements.