Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Dodecahedral Edge Length of Truncated Dodecahedron = sqrt(5)*(12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
le(Dodecahedron) = sqrt(5)*(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
Dodecahedral Edge Length of Truncated Dodecahedron - (Measured in Meter) - Dodecahedral Edge Length of Truncated Dodecahedron is the length of any edge of the larger dodecahedron from which the corners are cut to form 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(Dodecahedron) = sqrt(5)*(12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(RA/V*(99+(47*sqrt(5)))) --> sqrt(5)*(12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5))))
Evaluating ... ...
le(Dodecahedron) = 26.5549265712418
STEP 3: Convert Result to Output's Unit
26.5549265712418 Meter --> No Conversion Required
FINAL ANSWER
26.5549265712418 26.55493 Meter <-- Dodecahedral Edge Length of Truncated Dodecahedron
(Calculation completed in 00.020 seconds)

Credits

Creator Image
Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has created this Calculator and 2000+ more calculators!
Verifier Image
Verified by Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has verified this Calculator and 1100+ more calculators!

Dodecahedral Edge Length of Truncated Dodecahedron Calculators

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

Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio Formula

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

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

How to calculate Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Dodecahedral 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 Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 26.55493 = sqrt(5)*(12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5)))).

FAQ

What is Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio?
Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the larger dodecahedron from which the corners are cut to form the Truncated Dodecahedron, and calculated using the surface to volume ratio of the Truncated Dodecahedron and is represented as le(Dodecahedron) = sqrt(5)*(12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(RA/V*(99+(47*sqrt(5)))) or Dodecahedral Edge Length of Truncated Dodecahedron = sqrt(5)*(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 Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio?
Dodecahedral Edge Length of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the larger dodecahedron from which the corners are cut to form the Truncated Dodecahedron, and calculated using the surface to volume ratio of the Truncated Dodecahedron is calculated using Dodecahedral Edge Length of Truncated Dodecahedron = sqrt(5)*(12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))). To calculate Dodecahedral 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 Dodecahedral Edge Length of Truncated Dodecahedron?
In this formula, Dodecahedral 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 -
  • Dodecahedral Edge Length of Truncated Dodecahedron = sqrt(5)*Edge Length of Truncated Dodecahedron
  • Dodecahedral Edge Length of Truncated Dodecahedron = sqrt(Total Surface Area of Truncated Dodecahedron/(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))
  • Dodecahedral Edge Length of Truncated Dodecahedron = sqrt(5)*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!