Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5))))
RA/V = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*rc)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5))))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Surface to Volume Ratio of Truncated Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Truncated Dodecahedron is the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron.
Circumsphere Radius of Truncated Dodecahedron - (Measured in Meter) - Circumsphere Radius of Truncated Dodecahedron is the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere.
STEP 1: Convert Input(s) to Base Unit
Circumsphere Radius of Truncated Dodecahedron: 30 Meter --> 30 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*rc)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5)))) --> (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*30)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5))))
Evaluating ... ...
RA/V = 0.11754785836381
STEP 3: Convert Result to Output's Unit
0.11754785836381 1 per Meter --> No Conversion Required
FINAL ANSWER
0.11754785836381 0.117548 1 per Meter <-- Surface to Volume Ratio of Truncated Dodecahedron
(Calculation completed in 00.021 seconds)

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Surface to Volume Ratio of Truncated Dodecahedron Calculators

Surface to Volume Ratio of Truncated Dodecahedron given Total Surface Area
​ LaTeX ​ Go Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))*(99+(47*sqrt(5))))
Surface to Volume Ratio of Truncated Dodecahedron given Volume
​ LaTeX ​ Go Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)*(99+(47*sqrt(5))))
Surface to Volume Ratio of Truncated Dodecahedron given Dodecahedral Edge Length
​ LaTeX ​ Go Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)*(99+(47*sqrt(5))))
Surface to Volume Ratio of Truncated Dodecahedron
​ LaTeX ​ Go Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Edge Length of Truncated Dodecahedron*(99+(47*sqrt(5))))

Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius Formula

​LaTeX ​Go
Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5))))
RA/V = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*rc)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5))))

What is a Truncated Dodecahedron?

In geometry, the Truncated Dodecahedron is an Archimedean solid. It has a total of 32 faces - 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Each vertex is identical in such a way that two decagonal faces and one triangular face join at each vertex. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. The Truncated Dodecahedron has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: hexagonal and pentagonal.

How to Calculate Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius?

Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius calculator uses Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5)))) to calculate the Surface to Volume Ratio of Truncated Dodecahedron, Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron. Surface to Volume Ratio of Truncated Dodecahedron is denoted by RA/V symbol.

How to calculate Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Dodecahedron (rc) and hit the calculate button. Here is how the Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 0.117548 = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*30)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5)))).

FAQ

What is Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius?
Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron and is represented as RA/V = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*rc)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5)))) or Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5)))). Circumsphere Radius of Truncated Dodecahedron is the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere.
How to calculate Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius?
Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron is calculated using Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))*(99+(47*sqrt(5)))). To calculate Surface to Volume Ratio of Truncated Dodecahedron given Circumsphere Radius, you need Circumsphere Radius of Truncated Dodecahedron (rc). With our tool, you need to enter the respective value for Circumsphere Radius of Truncated Dodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Surface to Volume Ratio of Truncated Dodecahedron?
In this formula, Surface to Volume Ratio of Truncated Dodecahedron uses Circumsphere Radius of Truncated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Edge Length of Truncated Dodecahedron*(99+(47*sqrt(5))))
  • Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)*(99+(47*sqrt(5))))
  • Surface to Volume Ratio of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))*(99+(47*sqrt(5))))
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