Edge Length of Truncated Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
le = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(RA/V*(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
Edge Length of Truncated Dodecahedron - (Measured in Meter) - Edge Length of Truncated Dodecahedron is the length of any edge of the Truncated Dodecahedron.
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.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Truncated Dodecahedron: 0.1 1 per Meter --> 0.1 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
le = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(RA/V*(99+(47*sqrt(5)))) --> (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5))))
Evaluating ... ...
le = 11.8757241901624
STEP 3: Convert Result to Output's Unit
11.8757241901624 Meter --> No Conversion Required
FINAL ANSWER
11.8757241901624 11.87572 Meter <-- Edge Length of Truncated Dodecahedron
(Calculation completed in 00.008 seconds)

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Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
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Walchand College of Engineering (WCE), Sangli
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Edge Length of Truncated Dodecahedron Calculators

Edge Length of Truncated Dodecahedron given Total Surface Area
​ LaTeX ​ Go Edge Length of Truncated Dodecahedron = sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
Edge Length of Truncated Dodecahedron given Circumsphere Radius
​ LaTeX ​ Go Edge Length of Truncated Dodecahedron = (4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5))))
Edge Length of Truncated Dodecahedron given Volume
​ LaTeX ​ Go Edge Length of Truncated Dodecahedron = ((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
Edge Length of Truncated Dodecahedron given Dodecahedral Edge Length
​ LaTeX ​ Go Edge Length of Truncated Dodecahedron = Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)

Edge Length of Truncated Dodecahedron given Surface to Volume Ratio Formula

​LaTeX ​Go
Edge Length of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
le = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(RA/V*(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 Edge Length of Truncated Dodecahedron given Surface to Volume Ratio?

Edge Length of Truncated Dodecahedron given Surface to Volume Ratio calculator uses Edge Length of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))) to calculate the Edge Length of Truncated Dodecahedron, Edge Length of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Truncated Dodecahedron, and calculated using the surface to volume ratio of the Truncated Dodecahedron. Edge Length of Truncated Dodecahedron is denoted by le symbol.

How to calculate Edge Length of Truncated Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Edge Length of Truncated Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Truncated Dodecahedron (RA/V) and hit the calculate button. Here is how the Edge Length of Truncated Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 11.87572 = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5)))).

FAQ

What is Edge Length of Truncated Dodecahedron given Surface to Volume Ratio?
Edge Length of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Truncated Dodecahedron, and calculated using the surface to volume ratio of the Truncated Dodecahedron and is represented as le = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(RA/V*(99+(47*sqrt(5)))) or Edge Length of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))). 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.
How to calculate Edge Length of Truncated Dodecahedron given Surface to Volume Ratio?
Edge Length of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Truncated Dodecahedron, and calculated using the surface to volume ratio of the Truncated Dodecahedron is calculated using Edge Length of Truncated Dodecahedron = (12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))). To calculate Edge Length of Truncated Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Truncated Dodecahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Edge Length of Truncated Dodecahedron?
In this formula, Edge Length of Truncated Dodecahedron uses Surface to Volume Ratio of Truncated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Edge Length of Truncated Dodecahedron = Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
  • Edge Length of Truncated Dodecahedron = sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))
  • Edge Length of Truncated Dodecahedron = ((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
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