1. What is Surface to Volume Ratio of Dodecahedron?

The Surface to Volume Ratio of a Dodecahedron is a geometric measurement that compares the total surface area to the volume of this twelve-faced polyhedron. It's an important parameter in various scientific and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Insphere Radius — The radius of the sphere inscribed within the dodecahedron (m)

Explanation: This formula calculates the ratio of surface area to volume based on the insphere radius of a regular dodecahedron.

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. It affects properties like heat transfer, chemical reactivity, and structural efficiency.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and non-zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).

5. Frequently Asked Questions (FAQ)

Q1: What is a dodecahedron?
A: A dodecahedron is a three-dimensional shape with twelve flat faces, each being a regular pentagon.

Q2: What is insphere radius?
A: The insphere radius is the radius of the largest sphere that can fit inside the dodecahedron, touching all faces.

Q3: Why is surface to volume ratio important?
A: This ratio is critical in understanding how physical properties scale with size, particularly in nanoscale materials and biological systems.

Q4: What are typical values for this ratio?
A: The ratio depends on the size of the dodecahedron. Smaller dodecahedrons have higher surface to volume ratios.

Q5: Can this calculator be used for irregular dodecahedrons?
A: No, this calculator is specifically designed for regular dodecahedrons where all faces are identical regular pentagons.