Total Surface Area 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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✖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 Midsphere Radius [TSA]

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Total Surface Area of Snub Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
TSA = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/sqrt(1/(1-0.94315125924)))^2
This formula uses 1 Functions, 2 Variables

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.
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

TSA = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/sqrt(1/(1-0.94315125924)))^2 --> ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*21)/sqrt(1/(1-0.94315125924)))^2

Evaluating ... ...

TSA = 5544.21995095455

STEP 3: Convert Result to Output's Unit

5544.21995095455 Square Meter --> No Conversion Required

FINAL ANSWER

5544.21995095455 ≈ 5544.22 Square Meter <-- Total Surface Area of Snub Dodecahedron

(Calculation completed in 00.004 seconds)

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< Total Surface Area of Snub Dodecahedron Calculators

Total Surface Area of Snub Dodecahedron given Volume

LaTeX 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

LaTeX 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

LaTeX 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

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

< Important Formulas of Snub Dodecahedron Calculators

Surface to Volume Ratio of Snub Dodecahedron

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))/(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)))

Total Surface Area of Snub Dodecahedron

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

Circumsphere Radius of Snub Dodecahedron

LaTeX Go Circumsphere Radius of Snub Dodecahedron = sqrt((2-0.94315125924)/(1-0.94315125924))/2*Edge Length of Snub Dodecahedron

Midsphere Radius of Snub Dodecahedron

LaTeX Go Midsphere Radius of Snub Dodecahedron = sqrt(1/(1-0.94315125924))/2*Edge Length of Snub Dodecahedron

Total Surface Area 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 Total Surface Area of Snub Dodecahedron given Midsphere Radius?

Total Surface Area of Snub Dodecahedron given Midsphere Radius calculator uses 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 to calculate the Total Surface Area of Snub Dodecahedron, Total Surface Area of Snub Dodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron, and calculated using the midsphere radius 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 Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Snub Dodecahedron given Midsphere Radius, enter Midsphere Radius of Snub Dodecahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Snub Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 5544.22 = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*21)/sqrt(1/(1-0.94315125924)))^2.

FAQ

What is Total Surface Area of Snub Dodecahedron given Midsphere Radius?

Total Surface Area of Snub Dodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron and is represented as TSA = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/sqrt(1/(1-0.94315125924)))^2 or 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. 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 Total Surface Area of Snub Dodecahedron given Midsphere Radius?

Total Surface Area of Snub Dodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron is calculated using 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. To calculate Total Surface Area 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 Total Surface Area of Snub Dodecahedron?

In this formula, Total Surface Area 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 -

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

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