Total Surface Area of Snub Dodecahedron given Volume Calculator

✖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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✖Total Surface Area of Snub Dodecahedron is the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron.ⓘ Total Surface Area of Snub Dodecahedron given Volume [TSA]

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Formula

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Total Surface Area of Snub Dodecahedron given Volume

Formula

`"TSA" = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*(("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)))^(2/3)`

Example

`"5566.173m²"=((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*(("38000m³"*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)))^(2/3)`

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Total Surface Area of Snub Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3)
TSA = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3)
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

Total Surface Area of Snub Dodecahedron - (Measured in Square Meter) - Total Surface Area of Snub Dodecahedron is the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron.
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

TSA = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3) --> ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3)

Evaluating ... ...

TSA = 5566.17267755386

STEP 3: Convert Result to Output's Unit

5566.17267755386 Square Meter --> No Conversion Required

FINAL ANSWER

5566.17267755386 ≈ 5566.173 Square Meter <-- Total Surface Area of Snub Dodecahedron

(Calculation completed in 00.004 seconds)

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< 5 Total Surface Area of Snub Dodecahedron Calculators

Total Surface Area of Snub Dodecahedron given Surface to Volume Ratio

Go Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((((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))/(Surface to Volume Ratio 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))))^2

Total Surface Area of Snub Dodecahedron given Volume

Go Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3)

Total Surface Area of Snub Dodecahedron given Circumsphere Radius

Go Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Circumsphere Radius of Snub Dodecahedron)/sqrt((2-0.94315125924)/(1-0.94315125924)))^2

Total Surface Area of Snub Dodecahedron given Midsphere Radius

Go Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)))^2

Total Surface Area of Snub Dodecahedron

Go Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Edge Length of Snub Dodecahedron^2

Total Surface Area of Snub Dodecahedron given Volume Formula

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 Total Surface Area of Snub Dodecahedron given Volume?

Total Surface Area of Snub Dodecahedron given Volume calculator uses Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3) to calculate the Total Surface Area of Snub Dodecahedron, Total Surface Area of Snub Dodecahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron, and calculated using the volume of the Snub Dodecahedron. Total Surface Area of Snub Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Snub Dodecahedron given Volume using this online calculator? To use this online calculator for Total Surface Area of Snub Dodecahedron given Volume, enter Volume of Snub Dodecahedron (V) and hit the calculate button. Here is how the Total Surface Area of Snub Dodecahedron given Volume calculation can be explained with given input values -> 5566.173 = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3).

FAQ

What is Total Surface Area of Snub Dodecahedron given Volume?

Total Surface Area of Snub Dodecahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron, and calculated using the volume of the Snub Dodecahedron and is represented as TSA = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3) or Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3). Volume of Snub Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Snub Dodecahedron.

How to calculate Total Surface Area of Snub Dodecahedron given Volume?

Total Surface Area of Snub Dodecahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron, and calculated using the volume of the Snub Dodecahedron is calculated using Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((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)))^(2/3). To calculate Total Surface Area 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 Total Surface Area of Snub Dodecahedron?

In this formula, Total Surface Area of Snub Dodecahedron uses Volume of Snub Dodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Edge Length of Snub Dodecahedron^2
Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Circumsphere Radius of Snub Dodecahedron)/sqrt((2-0.94315125924)/(1-0.94315125924)))^2
Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)))^2
Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((((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))/(Surface to Volume Ratio 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))))^2

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