Space Diagonal of Diagonally Halved Cylinder given Lateral Surface Area and Height Calculator

Formula Used:

\[ d_{Space} = \sqrt{h^2 + \left( \frac{2 \times LSA}{\pi \times h} \right)^2} \]

Space Diagonal of Diagonally Halved Cylinder:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Space Diagonal of Diagonally Halved Cylinder?

The Space Diagonal of Diagonally Halved Cylinder is the length of the major axis or the longest chord of the upper elliptical face of the Diagonally Halved Cylinder. It represents the longest straight line that can be drawn within the three-dimensional shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Space} = \sqrt{h^2 + \left( \frac{2 \times LSA}{\pi \times h} \right)^2} \]

Where:

\( d_{Space} \) — Space Diagonal of Diagonally Halved Cylinder (m)
\( h \) — Height of Diagonally Halved Cylinder (m)
\( LSA \) — Lateral Surface Area of Diagonally Halved Cylinder (m²)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: This formula calculates the space diagonal by combining the height of the cylinder with the derived radius from the lateral surface area.

3. Importance of Space Diagonal Calculation

Details: Calculating the space diagonal is important in geometric analysis, structural engineering, and 3D modeling applications where understanding the maximum internal dimensions of a diagonally halved cylinder is crucial.

4. Using the Calculator

Tips: Enter the height in meters and lateral surface area in square meters. All values must be positive numbers greater than zero.

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 an elliptical cross-section.

Q2: Why is the space diagonal important?
A: The space diagonal represents the longest possible measurement within the shape, which is important for packaging, structural analysis, and spatial planning.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise when using the exact values of height and lateral surface area.

Q4: Can this formula be used for any diagonally halved cylinder?
A: Yes, this formula applies to all right circular cylinders that have been diagonally halved.

Q5: What units should I use for the inputs?
A: The calculator uses meters for height and square meters for lateral surface area, but any consistent unit system can be used as long as all measurements are in the same units.