Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius Calculator

✖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 [r_m]

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✖Surface to Volume Ratio of Snub Dodecahedron is the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron.ⓘ Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius [R_A/V]

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Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924))*(((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)))
R_A/V = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*r_m)/sqrt(1/(1-0.94315125924))*(((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)))
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

Surface to Volume Ratio of Snub Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Snub Dodecahedron is the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron.
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.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Snub Dodecahedron: 21 Meter --> 21 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*r_m)/sqrt(1/(1-0.94315125924))*(((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))) --> (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*21)/sqrt(1/(1-0.94315125924))*(((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)))

Evaluating ... ...

R_A/V = 0.146767937253493

STEP 3: Convert Result to Output's Unit

0.146767937253493 1 per Meter --> No Conversion Required

FINAL ANSWER

0.146767937253493 ≈ 0.146768 1 per Meter <-- Surface to Volume Ratio of Snub Dodecahedron

(Calculation completed in 00.004 seconds)

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< Surface to Volume Ratio of Snub Dodecahedron Calculators

Surface to Volume Ratio of Snub Dodecahedron given Volume

LaTeX Go Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((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)*(((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)))

Surface to Volume Ratio of Snub Dodecahedron given Total Surface Area

LaTeX Go Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))*(((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)))

Surface to Volume Ratio of Snub Dodecahedron given Circumsphere Radius

LaTeX Go Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*Circumsphere Radius of Snub Dodecahedron)/sqrt((2-0.94315125924)/(1-0.94315125924))*(((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)))

Surface to Volume Ratio of Snub Dodecahedron

Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius Formula

LaTeX Go

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 Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius?

Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius calculator uses Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924))*(((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))) to calculate the Surface to Volume Ratio of Snub Dodecahedron, Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius formula is defined as the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron. Surface to Volume Ratio of Snub Dodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius, enter Midsphere Radius of Snub Dodecahedron (r_m) and hit the calculate button. Here is how the Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 0.146768 = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*21)/sqrt(1/(1-0.94315125924))*(((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))).

FAQ

What is Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius?

Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius formula is defined as the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron and is represented as R_A/V = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*r_m)/sqrt(1/(1-0.94315125924))*(((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))) or Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924))*(((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))). 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.

How to calculate Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius?

Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius formula is defined as the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron is calculated using Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924))*(((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))). To calculate Surface to Volume Ratio of Snub Dodecahedron given Midsphere Radius, you need Midsphere Radius of Snub Dodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius 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 Surface to Volume Ratio of Snub Dodecahedron?

In this formula, Surface to Volume Ratio of Snub Dodecahedron uses Midsphere Radius of Snub Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(Edge Length of Snub Dodecahedron*(((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)))
Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))*(((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)))
Surface to Volume Ratio of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((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)*(((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)))

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