Home Back

Volume of Elongated Dodecahedron given Height Calculator

Formula Used:

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

m

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is the Volume of Elongated Dodecahedron?

The volume of an elongated dodecahedron represents the total three-dimensional space enclosed by its surface. It's a polyhedron with 12 faces that has been elongated along one axis.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Explanation: This formula calculates the volume based on the height measurement of the elongated dodecahedron, using the mathematical relationship between height and volume for this specific geometric shape.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in material estimation, space planning, and understanding geometric properties.

4. Using the Calculator

Tips: Enter the height of the elongated dodecahedron in meters. The value must be positive and valid. The calculator will compute the volume using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron with 12 faces that has been extended or stretched along one axis, creating a longer shape while maintaining its dodecahedral properties.

Q2: Why is the square root of 3 used in the formula?
A: The square root of 3 appears in geometric formulas involving equilateral triangles and regular polyhedra, representing fundamental mathematical relationships in three-dimensional geometry.

Q3: Can this formula be used for other dodecahedron variations?
A: No, this specific formula applies only to the elongated dodecahedron. Other dodecahedron variations have different volume formulas based on their specific geometric properties.

Q4: What are the practical applications of this calculation?
A: This calculation is useful in crystallography, architectural design, 3D modeling, and any field dealing with complex geometric shapes and their volumetric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input height value. The accuracy depends on the precision of the height measurement provided.

Volume of Elongated Dodecahedron given Height Calculator© - All Rights Reserved 2025