Insphere Radius of Pentakis Dodecahedron given Midsphere Radius Calculator

✖Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Pentakis Dodecahedron [r_m]

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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 given Midsphere Radius [r_i]

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Insphere Radius of Pentakis Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))
r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*r_m)/(3+sqrt(5)))
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.
Midsphere Radius of Pentakis Dodecahedron - (Measured in Meter) - Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Pentakis Dodecahedron: 13 Meter --> 13 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*r_m)/(3+sqrt(5))) --> (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*13)/(3+sqrt(5)))

Evaluating ... ...

r_i = 12.7326171113234

STEP 3: Convert Result to Output's Unit

12.7326171113234 Meter --> No Conversion Required

FINAL ANSWER

12.7326171113234 ≈ 12.73262 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

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Indian Institute of Information Technology (IIIT), Bhopal

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< Insphere Radius of Pentakis Dodecahedron Calculators

Insphere Radius of Pentakis Dodecahedron given Total Surface Area

LaTeX 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

LaTeX 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 Leg Length

LaTeX 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

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

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius Formula

LaTeX Go

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 given Midsphere Radius?

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius calculator uses Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5))) to calculate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Midsphere Radius 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, calculated using the midsphere radius of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Pentakis Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Insphere Radius of Pentakis Dodecahedron given Midsphere Radius, enter Midsphere Radius of Pentakis Dodecahedron (r_m) and hit the calculate button. Here is how the Insphere Radius of Pentakis Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 12.73262 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*13)/(3+sqrt(5))).

FAQ

What is Insphere Radius of Pentakis Dodecahedron given Midsphere Radius?

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius 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, calculated using the midsphere radius of the Pentakis Dodecahedron and is represented as r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*r_m)/(3+sqrt(5))) or Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5))). Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.

How to calculate Insphere Radius of Pentakis Dodecahedron given Midsphere Radius?

Insphere Radius of Pentakis Dodecahedron given Midsphere Radius 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, calculated using the midsphere radius of the Pentakis Dodecahedron is calculated using Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5))). To calculate Insphere Radius of Pentakis Dodecahedron given Midsphere Radius, you need Midsphere Radius of Pentakis Dodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Insphere Radius of Pentakis Dodecahedron?

In this formula, Insphere Radius of Pentakis Dodecahedron uses Midsphere Radius of Pentakis Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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