Insphere Radius of Pentakis Dodecahedron Calculator

✖Base Length of Pentakis Dodecahedron is the length of the base of the isosceles triangular face of Pentakis Dodecahedron.ⓘ Base Length of Pentakis Dodecahedron [l_Base]

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✖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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Formula

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Insphere Radius of Pentakis Dodecahedron

Formula

`"r"_{"i"} = ((3*(sqrt((81+(35*sqrt(5)))/218)))*"l"_{"Base"})/2`

Example

`"12.82093m"=((3*(sqrt((81+(35*sqrt(5)))/218)))*"10m")/2`

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Insphere Radius of Pentakis Dodecahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2
r_i = ((3*(sqrt((81+(35*sqrt(5)))/218)))*l_Base)/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

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.
Base Length of Pentakis Dodecahedron - (Measured in Meter) - Base Length of Pentakis Dodecahedron is the length of the base of the isosceles triangular face of Pentakis Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Base Length of Pentakis Dodecahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((3*(sqrt((81+(35*sqrt(5)))/218)))*l_Base)/2 --> ((3*(sqrt((81+(35*sqrt(5)))/218)))*10)/2

Evaluating ... ...

r_i = 12.8209324473781

STEP 3: Convert Result to Output's Unit

12.8209324473781 Meter --> No Conversion Required

FINAL ANSWER

12.8209324473781 ≈ 12.82093 Meter <-- Insphere Radius of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 6 Insphere Radius of Pentakis Dodecahedron Calculators

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio

Go Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))* ((76/19)/Surface to Volume Ratio of Pentakis Dodecahedron)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))

Insphere Radius of Pentakis Dodecahedron given Total Surface Area

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

Insphere Radius of Pentakis Dodecahedron given Volume

Go Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius

Go Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))

Insphere Radius of Pentakis Dodecahedron given Leg Length

Go Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))

Insphere Radius of Pentakis Dodecahedron

Go Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2

Insphere Radius of Pentakis Dodecahedron Formula

Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2
r_i = ((3*(sqrt((81+(35*sqrt(5)))/218)))*l_Base)/2

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 Insphere Radius of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron calculator uses Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2 to calculate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron formula is defined as 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 is denoted by r_i symbol.

How to calculate Insphere Radius of Pentakis Dodecahedron using this online calculator? To use this online calculator for Insphere Radius of Pentakis Dodecahedron, enter Base Length of Pentakis Dodecahedron (l_Base) and hit the calculate button. Here is how the Insphere Radius of Pentakis Dodecahedron calculation can be explained with given input values -> 12.82093 = ((3*(sqrt((81+(35*sqrt(5)))/218)))*10)/2.

FAQ

What is Insphere Radius of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron formula is defined as the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere and is represented as r_i = ((3*(sqrt((81+(35*sqrt(5)))/218)))*l_Base)/2 or Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2. Base Length of Pentakis Dodecahedron is the length of the base of the isosceles triangular face of Pentakis Dodecahedron.

How to calculate Insphere Radius of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron formula is defined as the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere is calculated using Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2. To calculate Insphere Radius of Pentakis Dodecahedron, you need Base Length of Pentakis Dodecahedron (l_Base). With our tool, you need to enter the respective value for Base Length 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 Insphere Radius of Pentakis Dodecahedron?

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

Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))
Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))
Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))
Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))* ((76/19)/Surface to Volume Ratio of Pentakis Dodecahedron)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))

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