Volume of Snub Dodecahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Snub Dodecahedron is the radius of the sphere that contains the Snub Dodecahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Snub Dodecahedron [r_c]

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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 given Circumsphere Radius [V]

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Volume of Snub Dodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume 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))/(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)))^3
V = (((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))/(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_c)/sqrt((2-0.94315125924)/(1-0.94315125924)))^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

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.
Circumsphere Radius of Snub Dodecahedron - (Measured in Meter) - Circumsphere Radius of Snub Dodecahedron is the radius of the sphere that contains the Snub Dodecahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Snub Dodecahedron: 22 Meter --> 22 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (((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))/(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_c)/sqrt((2-0.94315125924)/(1-0.94315125924)))^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))/(6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))*((2*22)/sqrt((2-0.94315125924)/(1-0.94315125924)))^3

Evaluating ... ...

V = 39976.0765151654

STEP 3: Convert Result to Output's Unit

39976.0765151654 Cubic Meter --> No Conversion Required

FINAL ANSWER

39976.0765151654 ≈ 39976.08 Cubic Meter <-- Volume of Snub Dodecahedron

(Calculation completed in 00.020 seconds)

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< Volume of Snub Dodecahedron Calculators

Volume of Snub Dodecahedron given Total Surface Area

LaTeX Go Volume 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))/(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)))))))^3

Volume of Snub Dodecahedron given Circumsphere Radius

LaTeX Go Volume 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))/(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)))^3

Volume of Snub Dodecahedron given Midsphere Radius

LaTeX Go Volume 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))/(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)))^3

Volume of Snub Dodecahedron

Volume of Snub Dodecahedron given Circumsphere 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 Volume of Snub Dodecahedron given Circumsphere Radius?

Volume of Snub Dodecahedron given Circumsphere Radius calculator uses Volume 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))/(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)))^3 to calculate the Volume of Snub Dodecahedron, Volume of Snub Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Snub Dodecahedron, and calculated using the circumsphere radius of the Snub Dodecahedron. Volume of Snub Dodecahedron is denoted by V symbol.

How to calculate Volume of Snub Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Volume of Snub Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Snub Dodecahedron (r_c) and hit the calculate button. Here is how the Volume of Snub Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 39976.08 = (((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))/(6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))*((2*22)/sqrt((2-0.94315125924)/(1-0.94315125924)))^3.

FAQ

What is Volume of Snub Dodecahedron given Circumsphere Radius?

Volume of Snub Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Snub Dodecahedron, and calculated using the circumsphere radius of the Snub Dodecahedron and is represented as V = (((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))/(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_c)/sqrt((2-0.94315125924)/(1-0.94315125924)))^3 or Volume 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))/(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)))^3. Circumsphere Radius of Snub Dodecahedron is the radius of the sphere that contains the Snub Dodecahedron in such a way that all the vertices are lying on the sphere.

How to calculate Volume of Snub Dodecahedron given Circumsphere Radius?

Volume of Snub Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Snub Dodecahedron, and calculated using the circumsphere radius of the Snub Dodecahedron is calculated using Volume 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))/(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)))^3. To calculate Volume of Snub Dodecahedron given Circumsphere Radius, you need Circumsphere Radius of Snub Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere 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 Volume of Snub Dodecahedron?

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

Volume 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))/(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^3
Volume 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))/(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)))))))^3
Volume 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))/(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)))^3

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