Midsphere Radius 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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✖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 given Insphere Radius [r_m]

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Midsphere Radius of Pentakis Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

r_m = ((3+sqrt(5))/4)*((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218)))) --> ((3+sqrt(5))/4)*((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))

Evaluating ... ...

r_m = 12.2519980484818

STEP 3: Convert Result to Output's Unit

12.2519980484818 Meter --> No Conversion Required

FINAL ANSWER

12.2519980484818 ≈ 12.252 Meter <-- Midsphere Radius of Pentakis Dodecahedron

(Calculation completed in 00.007 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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< Midsphere Radius of Pentakis Dodecahedron Calculators

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio

LaTeX Go Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))

Midsphere Radius of Pentakis Dodecahedron given Total Surface Area

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

Midsphere Radius of Pentakis Dodecahedron given Leg Length

LaTeX Go Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))

Midsphere Radius of Pentakis Dodecahedron

LaTeX Go Midsphere Radius of Pentakis Dodecahedron = (Base Length of Pentakis Dodecahedron/4)*(3+sqrt(5))

Midsphere Radius of Pentakis Dodecahedron given Insphere Radius Formula

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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 Midsphere Radius of Pentakis Dodecahedron given Insphere Radius?

Midsphere Radius of Pentakis Dodecahedron given Insphere Radius calculator uses Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218)))) to calculate the Midsphere Radius of Pentakis Dodecahedron, Midsphere Radius of Pentakis Dodecahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere, calculated using the insphere radius of the Pentakis Dodecahedron. Midsphere Radius of Pentakis Dodecahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Pentakis Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Pentakis Dodecahedron given Insphere Radius, enter Insphere Radius of Pentakis Dodecahedron (r_i) and hit the calculate button. Here is how the Midsphere Radius of Pentakis Dodecahedron given Insphere Radius calculation can be explained with given input values -> 12.252 = ((3+sqrt(5))/4)*((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218)))).

FAQ

What is Midsphere Radius of Pentakis Dodecahedron given Insphere Radius?

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

Midsphere Radius of Pentakis Dodecahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere, calculated using the insphere radius of the Pentakis Dodecahedron is calculated using Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218)))). To calculate Midsphere Radius 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 Midsphere Radius of Pentakis Dodecahedron?

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

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

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