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Midsphere Radius of Snub Dodecahedron given Volume Calculator

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✖Volume of Snub Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Snub Dodecahedron.ⓘ Volume of Snub Dodecahedron [V]
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✖Midsphere Radius of Snub Dodecahedron is the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Snub Dodecahedron given Volume [rm]
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Midsphere Radius of Snub Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)
rm = sqrt(1/(1-0.94315125924))/2*((V*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)
This formula uses 1 Constants, 1 Functions, 2 Variables
Constants Used
[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811
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
Midsphere Radius of Snub Dodecahedron - (Measured in Meter) - Midsphere Radius of Snub Dodecahedron is the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere.
Volume of Snub Dodecahedron - (Measured in Cubic Meter) - Volume of Snub Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Snub Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Volume of Snub Dodecahedron: 38000 Cubic Meter --> 38000 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(1/(1-0.94315125924))/2*((V*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3) --> sqrt(1/(1-0.94315125924))/2*((38000*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)
Evaluating ... ...
rm = 21.041534410276
STEP 3: Convert Result to Output's Unit
21.041534410276 Meter --> No Conversion Required
FINAL ANSWER
21.041534410276 ≈ 21.04153 Meter <-- Midsphere Radius of Snub Dodecahedron
(Calculation completed in 00.020 seconds)
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Midsphere Radius of Snub Dodecahedron Calculators

Midsphere Radius of Snub Dodecahedron given Volume
​ LaTeX ​ Go Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)
Midsphere Radius of Snub Dodecahedron given Total Surface Area
​ LaTeX ​ Go Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Midsphere Radius of Snub Dodecahedron given Circumsphere Radius
​ LaTeX ​ Go Midsphere Radius of Snub Dodecahedron = Circumsphere Radius of Snub Dodecahedron/sqrt(2-0.94315125924)
Midsphere Radius of Snub Dodecahedron
​ LaTeX ​ Go Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*Edge Length of Snub Dodecahedron

Midsphere Radius of Snub Dodecahedron given Volume Formula

​LaTeX ​Go
Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)
rm = sqrt(1/(1-0.94315125924))/2*((V*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)

What is a Snub Dodecahedron?

In geometry, the Snub Dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal non-prismatic 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. Each vertex is identical in such a way that, 4 equilateral triangular faces and 1 pentagonal face are joining together at each vertex. 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 Midsphere Radius of Snub Dodecahedron given Volume?

Midsphere Radius of Snub Dodecahedron given Volume calculator uses Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3) to calculate the Midsphere Radius of Snub Dodecahedron, Midsphere Radius of Snub Dodecahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere, and calculated using the volume of the Snub Dodecahedron. Midsphere Radius of Snub Dodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Snub Dodecahedron given Volume using this online calculator? To use this online calculator for Midsphere Radius of Snub Dodecahedron given Volume, enter Volume of Snub Dodecahedron (V) and hit the calculate button. Here is how the Midsphere Radius of Snub Dodecahedron given Volume calculation can be explained with given input values -> 21.04153 = sqrt(1/(1-0.94315125924))/2*((38000*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3).

FAQ

What is Midsphere Radius of Snub Dodecahedron given Volume?
Midsphere Radius of Snub Dodecahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere, and calculated using the volume of the Snub Dodecahedron and is represented as rm = sqrt(1/(1-0.94315125924))/2*((V*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3) or Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3). Volume of Snub Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Snub Dodecahedron.
How to calculate Midsphere Radius of Snub Dodecahedron given Volume?
Midsphere Radius of Snub Dodecahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere, and calculated using the volume of the Snub Dodecahedron is calculated using Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3). To calculate Midsphere Radius of Snub Dodecahedron given Volume, you need Volume of Snub Dodecahedron (V). With our tool, you need to enter the respective value for Volume of Snub 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 Midsphere Radius of Snub Dodecahedron?
In this formula, Midsphere Radius of Snub Dodecahedron uses Volume of Snub Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*Edge Length of Snub Dodecahedron
  • Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
  • Midsphere Radius of Snub Dodecahedron = Circumsphere Radius of Snub Dodecahedron/sqrt(2-0.94315125924)
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