Total Surface Area of Pentakis Dodecahedron given Insphere Radius Calculator

✖Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.ⓘ Insphere Radius of Pentakis Dodecahedron [r_i]

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✖Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.ⓘ Total Surface Area of Pentakis Dodecahedron given Insphere Radius [TSA]

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Total Surface Area of Pentakis Dodecahedron given Insphere Radius

Formula

`"TSA" = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*"r"_{"i"})/(3*(sqrt((81+(35*sqrt(5)))/218))))^2)`

Example

`"1925.661m²"=(15/19)*(sqrt(413+(162*sqrt(5))))*(((2*"12m")/(3*(sqrt((81+(35*sqrt(5)))/218))))^2)`

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Total Surface Area of Pentakis Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2)
TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218))))^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 Pentakis Dodecahedron - (Measured in Square Meter) - Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.
Insphere Radius of Pentakis Dodecahedron - (Measured in Meter) - Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Pentakis Dodecahedron: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2) --> (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2)

Evaluating ... ...

TSA = 1925.66109639037

STEP 3: Convert Result to Output's Unit

1925.66109639037 Square Meter --> No Conversion Required

FINAL ANSWER

1925.66109639037 ≈ 1925.661 Square Meter <-- Total Surface Area of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

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< 6 Surface Area of Pentakis Dodecahedron Calculators

Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio

Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2)

Total Surface Area of Pentakis Dodecahedron given Insphere Radius

Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2)

Total Surface Area of Pentakis Dodecahedron given Volume

Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(2/3))

Total Surface Area of Pentakis Dodecahedron given Midsphere Radius

Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^2)

Total Surface Area of Pentakis Dodecahedron given Leg Length

Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^2)

Total Surface Area of Pentakis Dodecahedron

Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(Base Length of Pentakis Dodecahedron^2)*(sqrt(413+(162*sqrt(5))))

Total Surface Area of Pentakis Dodecahedron given Insphere Radius Formula

What is Pentakis Dodecahedron?

A Pentakis Dodecahedron is a polyhedron with isosceles triangle faces. Five of these are attached as a pyramid on each face of a dodecahedron.
It has 60 faces, 90 edges, 32 vertices.

How to Calculate Total Surface Area of Pentakis Dodecahedron given Insphere Radius?

Total Surface Area of Pentakis Dodecahedron given Insphere Radius calculator uses Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2) to calculate the Total Surface Area of Pentakis Dodecahedron, Total Surface Area of Pentakis Dodecahedron given Insphere Radius formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron. Total Surface Area of Pentakis Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Pentakis Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Pentakis Dodecahedron given Insphere Radius, enter Insphere Radius of Pentakis Dodecahedron (r_i) and hit the calculate button. Here is how the Total Surface Area of Pentakis Dodecahedron given Insphere Radius calculation can be explained with given input values -> 1925.661 = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2).

FAQ

What is Total Surface Area of Pentakis Dodecahedron given Insphere Radius?

Total Surface Area of Pentakis Dodecahedron given Insphere Radius formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron and is represented as TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2) or Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2). Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.

How to calculate Total Surface Area of Pentakis Dodecahedron given Insphere Radius?

Total Surface Area of Pentakis Dodecahedron given Insphere Radius formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron is calculated using Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2). To calculate Total Surface Area of Pentakis Dodecahedron given Insphere Radius, you need Insphere Radius of Pentakis Dodecahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Pentakis 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 Pentakis Dodecahedron?

In this formula, Total Surface Area of Pentakis Dodecahedron uses Insphere Radius of Pentakis Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Pentakis Dodecahedron = (15/19)*(Base Length of Pentakis Dodecahedron^2)*(sqrt(413+(162*sqrt(5))))
Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^2)
Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(2/3))
Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^2)
Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2)

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