Height of Elongated Dodecahedron given Volume Calculator

Formula Used:

\[ h = \sqrt{3} \times \left( \frac{V}{6} \right)^{1/3} \]

Height of Elongated Dodecahedron:

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1. What is the Height of Elongated Dodecahedron given Volume?

The height of an elongated dodecahedron is the vertical distance from the highest point to the lowest point of the polyhedron. This calculator determines the height when the volume of the elongated dodecahedron is known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{3} \times \left( \frac{V}{6} \right)^{1/3} \]

Where:

\( h \) — Height of Elongated Dodecahedron (m)
\( V \) — Volume of Elongated Dodecahedron (m³)

Explanation: This formula uses the square root function and cube root function to calculate the height based on the given volume of the elongated dodecahedron.

3. Importance of Height Calculation

Details: Calculating the height of an elongated dodecahedron is important in geometry, architectural design, and various engineering applications where precise dimensional measurements are required.

4. Using the Calculator

Tips: Enter the volume of the elongated dodecahedron in cubic meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron with 12 faces that has been stretched along one axis, creating a longer dimension in one direction.

Q2: Why is the cube root used in this formula?
A: The cube root is used because volume is a cubic measurement, and we need to find the linear dimension (height) from the volumetric measurement.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula is derived for elongated dodecahedrons and may not apply to other polyhedral shapes.

Q4: What units should I use for the volume input?
A: The calculator expects volume in cubic meters, but you can use any consistent cubic units as long as you interpret the height result in the corresponding linear units.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect elongated dodecahedron shape. The accuracy depends on the precision of the volume measurement provided.