Height of Diagonally Halved Cylinder given Total Surface Area Calculator

Formula Used:

\[ h = \frac{TSA}{\pi \times r} - r - \frac{d_{Space}}{2} \]

Total Surface Area of Diagonally Halved Cylinder (TSA):

m²

Radius of Diagonally Halved Cylinder (r):

Space Diagonal of Diagonally Halved Cylinder (dSpace):

Height of Diagonally Halved Cylinder (h):

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1. What is the Height of Diagonally Halved Cylinder?

The Height of Diagonally Halved Cylinder is the vertical distance from the base circular face to the top most point of the Diagonally Halved Cylinder. It represents the maximum vertical extent of this three-dimensional geometric shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ h = \frac{TSA}{\pi \times r} - r - \frac{d_{Space}}{2} \]

Where:

\( h \) — Height of Diagonally Halved Cylinder (m)
\( TSA \) — Total Surface Area of Diagonally Halved Cylinder (m²)
\( r \) — Radius of Diagonally Halved Cylinder (m)
\( d_{Space} \) — Space Diagonal of Diagonally Halved Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

3. Formula Explanation

Details: This formula derives from the geometric properties of a diagonally halved cylinder. It relates the height to the total surface area, radius, and space diagonal through mathematical relationships specific to this particular geometric configuration.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, square meters for area). Ensure all input values are positive numbers. The calculator provides results with high precision (6 decimal places).

5. Frequently Asked Questions (FAQ)

Q1: What is a Diagonally Halved Cylinder?
A: A Diagonally Halved Cylinder is a cylinder that has been cut diagonally across its height, creating two identical wedge-shaped pieces with elliptical cross-sections.

Q2: Why is the space diagonal important in this calculation?
A: The space diagonal represents the longest distance between two points on the halved cylinder and is crucial for determining the geometric relationships in the formula.

Q3: What are typical applications of this calculation?
A: This calculation is used in engineering, architecture, and manufacturing where diagonally cut cylindrical components are involved, such as in piping systems or structural elements.

Q4: How accurate is this formula?
A: The formula is mathematically exact for perfect geometric shapes. Real-world accuracy depends on the precision of input measurements.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurements to meters before input, or adjust the result accordingly.