Total Surface Area of Triakis Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2)
TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*ri)/(sqrt((10*(33+(13*sqrt(5))))/61)))^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 Triakis Icosahedron - (Measured in Square Meter) - The Total Surface Area of Triakis Icosahedron is the amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron.
Insphere Radius of Triakis Icosahedron - (Measured in Meter) - Insphere Radius of Triakis Icosahedron is the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Triakis Icosahedron: 6 Meter --> 6 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*ri)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2) --> (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*6)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2)
Evaluating ... ...
TSA = 499.777880007178
STEP 3: Convert Result to Output's Unit
499.777880007178 Square Meter --> No Conversion Required
FINAL ANSWER
499.777880007178 499.7779 Square Meter <-- Total Surface Area of Triakis Icosahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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Indian Institute of Information Technology (IIIT), Bhopal
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6 Total Surface Area of Triakis Icosahedron Calculators

Total Surface Area of Triakis Icosahedron given Surface to Volume Ratio
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron))^2)
Total Surface Area of Triakis Icosahedron given Insphere Radius
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2)
Total Surface Area of Triakis Icosahedron given Pyramidal Edge Length
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))^2)
Total Surface Area of Triakis Icosahedron given Volume
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((44*Volume of Triakis Icosahedron)/(5*(5+(7*sqrt(5)))))^(2/3))
Total Surface Area of Triakis Icosahedron given Midsphere Radius
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2)
Total Surface Area of Triakis Icosahedron
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*((Icosahedral Edge Length of Triakis Icosahedron)^2)

Total Surface Area of Triakis Icosahedron given Insphere Radius Formula

Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2)
TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*ri)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2)

What is Triakis Icosahedron?

The Triakis Icosahedron is a three-dimensional polyhedron created from the dual of the truncated dodecahedron. Because of this, it shares the same full icosahedral symmetry group as the dodecahedron and the truncated dodecahedron. It can also be constructed by adding short triangular pyramids onto the faces of an icosahedron. It has 60 faces, 90 edges, 32 vertices.

How to Calculate Total Surface Area of Triakis Icosahedron given Insphere Radius?

Total Surface Area of Triakis Icosahedron given Insphere Radius calculator uses Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2) to calculate the Total Surface Area of Triakis Icosahedron, Total Surface Area of Triakis Icosahedron given Insphere Radius formula is defined asthe amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron, calculated using insphere radius of Triakis Icosahedon. Total Surface Area of Triakis Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Triakis Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Triakis Icosahedron given Insphere Radius, enter Insphere Radius of Triakis Icosahedron (ri) and hit the calculate button. Here is how the Total Surface Area of Triakis Icosahedron given Insphere Radius calculation can be explained with given input values -> 499.7779 = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*6)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2).

FAQ

What is Total Surface Area of Triakis Icosahedron given Insphere Radius?
Total Surface Area of Triakis Icosahedron given Insphere Radius formula is defined asthe amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron, calculated using insphere radius of Triakis Icosahedon and is represented as TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*ri)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2) or Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2). Insphere Radius of Triakis Icosahedron is the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere.
How to calculate Total Surface Area of Triakis Icosahedron given Insphere Radius?
Total Surface Area of Triakis Icosahedron given Insphere Radius formula is defined asthe amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron, calculated using insphere radius of Triakis Icosahedon is calculated using Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2). To calculate Total Surface Area of Triakis Icosahedron given Insphere Radius, you need Insphere Radius of Triakis Icosahedron (ri). With our tool, you need to enter the respective value for Insphere Radius of Triakis Icosahedron 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 Triakis Icosahedron?
In this formula, Total Surface Area of Triakis Icosahedron uses Insphere Radius of Triakis Icosahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*((Icosahedral Edge Length of Triakis Icosahedron)^2)
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))^2)
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((44*Volume of Triakis Icosahedron)/(5*(5+(7*sqrt(5)))))^(2/3))
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2)
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron))^2)
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