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)))
ri = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*rm)/(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
ri = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*rm)/(3+sqrt(5))) --> (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*13)/(3+sqrt(5)))
Evaluating ... ...
ri = 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)

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 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 given Midsphere Radius Formula

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

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 ri 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 (rm) 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 ri = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((4*rm)/(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 (rm). 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 5 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)))))))
  • 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))* ((76/19)/Surface to Volume Ratio of Pentakis Dodecahedron)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
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