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Circumradius of Snub Dodecahedron given surface to volume ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumradius = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
rc = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(RAV*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
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 = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(RAV*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 --> (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(0.5*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
Evaluating ... ...
rc = 0.38081331915839
STEP 3: Convert Result to Output's Unit
0.38081331915839 Meter --> No Conversion Required
FINAL ANSWER
0.38081331915839 Meter <-- Circumradius
(Calculation completed in 00.000 seconds)

5 Circumradius of Snub Dodecahedron Calculators

Circumradius of Snub Dodecahedron given surface to volume ratio
circumradius = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 Go
Circumradius of Snub Dodecahedron given surface area
circumradius = (sqrt(Surface Area/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 Go
Circumradius of Snub Dodecahedron given volume
circumradius = (((Volume*(6*sqrt(3-1.7155^2)^(3)))/(((12*(1.7155^2)*((3*1.6180)+1))-(1.7155*((36*1.6180)+7))-((53*1.6180)+6))))^(1/3))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 Go
Circumradius of Snub Dodecahedron given midradius
circumradius = ((2*Midradius)/(1.6180*(sqrt((1.8392*(1.8392+1.6180))+1))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 Go
Circumradius of Snub Dodecahedron
circumradius = Side*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 Go

Circumradius of Snub Dodecahedron given surface to volume ratio Formula

circumradius = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
rc = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(RAV*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2

What is a snub dodecahedron?

In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces. The snub dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two snub dodecahedra, and the convex hull of both forms is a truncated icosidodecahedron.

How to Calculate Circumradius of Snub Dodecahedron given surface to volume ratio?

Circumradius of Snub Dodecahedron given surface to volume ratio calculator uses circumradius = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 to calculate the Circumradius, Circumradius of Snub Dodecahedron given surface to volume ratio formula is defined as a straight line connecting center and any point of circumsphere of snub dodecahedron ,Where side= snub dodecahedron edge (a). Circumradius and is denoted by rc symbol.

How to calculate Circumradius of Snub Dodecahedron given surface to volume ratio using this online calculator? To use this online calculator for Circumradius of Snub Dodecahedron given surface to volume ratio, enter Surface to Volume Ratio (RAV) and hit the calculate button. Here is how the Circumradius of Snub Dodecahedron given surface to volume ratio calculation can be explained with given input values -> 0.380813 = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(0.5*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2.

FAQ

What is Circumradius of Snub Dodecahedron given surface to volume ratio?
Circumradius of Snub Dodecahedron given surface to volume ratio formula is defined as a straight line connecting center and any point of circumsphere of snub dodecahedron ,Where side= snub dodecahedron edge (a) and is represented as rc = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(RAV*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2 or circumradius = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2. Surface to Volume Ratio is fraction of surface to volume.
How to calculate Circumradius of Snub Dodecahedron given surface to volume ratio?
Circumradius of Snub Dodecahedron given surface to volume ratio formula is defined as a straight line connecting center and any point of circumsphere of snub dodecahedron ,Where side= snub dodecahedron edge (a) is calculated using circumradius = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2. To calculate Circumradius of Snub 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 5 other way(s) to calculate the same, which is/are as follows -
  • circumradius = Side*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
  • circumradius = (sqrt(Surface Area/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
  • circumradius = (((Volume*(6*sqrt(3-1.7155^2)^(3)))/(((12*(1.7155^2)*((3*1.6180)+1))-(1.7155*((36*1.6180)+7))-((53*1.6180)+6))))^(1/3))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
  • circumradius = ((2*Midradius)/(1.6180*(sqrt((1.8392*(1.8392+1.6180))+1))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
  • circumradius = (((6*sqrt(3-1.7155^2)^(3))*((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio*((12*(1.7155^2)*((3*1.6180)+1))-(0.9431*((36*1.6180)+7))-((53*1.6180)+6))))*1.6180*(sqrt((1.8392*(1.8392+1.6180))+(3-1.6180)))/2
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