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Surface To Volume Ratio Of Rhombic Triacontahedron Formula:
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The Surface to Volume Ratio of a Rhombic Triacontahedron is the numerical ratio of the total surface area to the volume of this polyhedron. A Rhombic Triacontahedron is a convex polyhedron with 30 rhombic faces, 32 vertices, and 60 edges.
The calculator uses the formula:
Where:
Explanation: This formula calculates how much surface area exists per unit volume of the Rhombic Triacontahedron, which is important in various physical and engineering applications.
Details: The surface to volume ratio is crucial in materials science, chemistry, and physics as it affects properties like reactivity, heat transfer, and strength-to-weight ratios in structures based on this geometry.
Tips: Enter the edge length of the Rhombic Triacontahedron in meters. The value must be positive and greater than zero.
Q1: What is a Rhombic Triacontahedron?
A: A Rhombic Triacontahedron is a polyhedron with 30 congruent rhombic faces. It's one of the Catalan solids and is the dual polyhedron of the icosidodecahedron.
Q2: What are the applications of this calculation?
A: This calculation is used in materials science, nanotechnology, crystal structures, and architectural design where this specific geometry is employed.
Q3: How does edge length affect the surface to volume ratio?
A: As the edge length increases, the surface to volume ratio decreases, following an inverse relationship typical of most geometric shapes.
Q4: What units should I use for the edge length?
A: The edge length should be in meters for SI units, but any consistent length unit can be used as the ratio will have dimensions of 1/length.
Q5: Can this formula be used for scaled models?
A: Yes, the formula works for any scale as long as the edge length measurement is consistent and accurate.