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Circumradius of Truncated Dodecahedron given surface to volume ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5))))
rc = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(RAV*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5))))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Surface to Volume Ratio - Surface to Volume Ratio is fraction of surface to volume. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio: 0.5 Hundred --> 0.5 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(RAV*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))) --> (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(0.5*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5))))
Evaluating ... ...
rc = 14.6591892860014
STEP 3: Convert Result to Output's Unit
14.6591892860014 Meter --> No Conversion Required
FINAL ANSWER
14.6591892860014 Meter <-- Circumradius
(Calculation completed in 00.000 seconds)

6 Circumradius of Truncated Dodecahedron Calculators

Circumradius of Truncated Dodecahedron given surface to volume ratio
circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given surface area
circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given volume
circumradius = ((((12*Volume)/(5*(99+47*sqrt(5))))^(1/3))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given midradius
circumradius = (((4*Midradius)/(5+(3*sqrt(5))))/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron given edge length dodecahedron
circumradius = (((sqrt(5)*Edge length)/5)/4)*(sqrt(74+(30*sqrt(5)))) Go
Circumradius of Truncated Dodecahedron
circumradius = (Side/4)*(sqrt(74+(30*sqrt(5)))) Go

Circumradius of Truncated Dodecahedron given surface to volume ratio Formula

circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5))))
rc = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(RAV*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5))))

What is a truncated dodecahedron?

In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. 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 Circumradius of Truncated Dodecahedron given surface to volume ratio?

Circumradius of Truncated Dodecahedron given surface to volume ratio calculator uses circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))) to calculate the Circumradius, The Circumradius of Truncated Dodecahedron given surface to volume ratio formula is defined as a straight line connecting center and any point of circumsphere of truncated cuboctahedron ,Where side= truncated dodecahedron edge (a). Circumradius and is denoted by rc symbol.

How to calculate Circumradius of Truncated Dodecahedron given surface to volume ratio using this online calculator? To use this online calculator for Circumradius of Truncated Dodecahedron given surface to volume ratio, enter Surface to Volume Ratio (RAV) and hit the calculate button. Here is how the Circumradius of Truncated Dodecahedron given surface to volume ratio calculation can be explained with given input values -> 14.65919 = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(0.5*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))).

FAQ

What is Circumradius of Truncated Dodecahedron given surface to volume ratio?
The Circumradius of Truncated Dodecahedron given surface to volume ratio formula is defined as a straight line connecting center and any point of circumsphere of truncated cuboctahedron ,Where side= truncated dodecahedron edge (a) and is represented as rc = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(RAV*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))) or circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))). Surface to Volume Ratio is fraction of surface to volume.
How to calculate Circumradius of Truncated Dodecahedron given surface to volume ratio?
The Circumradius of Truncated Dodecahedron given surface to volume ratio formula is defined as a straight line connecting center and any point of circumsphere of truncated cuboctahedron ,Where side= truncated dodecahedron edge (a) is calculated using circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5)))). To calculate Circumradius of Truncated Dodecahedron given surface to volume ratio, you need Surface to Volume Ratio (RAV). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Circumradius?
In this formula, Circumradius uses Surface to Volume Ratio. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • circumradius = (Side/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = (((sqrt(5)*Edge length)/5)/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = ((sqrt(Surface Area/(5*(sqrt(3)+(6*(sqrt(5)+2*sqrt(5)))))))/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = ((((12*Volume)/(5*(99+47*sqrt(5))))^(1/3))/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = (((4*Midradius)/(5+(3*sqrt(5))))/4)*(sqrt(74+(30*sqrt(5))))
  • circumradius = (((12*(sqrt(3)+(6*(sqrt(5)+(2*sqrt(5))))))/(Surface to Volume Ratio*((99+(47*sqrt(5))))))/4)*(sqrt(74+(30*sqrt(5))))
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