Leg Length 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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✖Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.ⓘ Leg Length of Pentakis Dodecahedron given Insphere Radius [l_Leg]

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Leg Length of Pentakis Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Leg Length of Pentakis Dodecahedron - (Measured in Meter) - Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face 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

l_Leg = (3/38)*(9+sqrt(5))*((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218)))) --> (3/38)*(9+sqrt(5))*((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))

Evaluating ... ...

l_Leg = 8.30259111213151

STEP 3: Convert Result to Output's Unit

8.30259111213151 Meter --> No Conversion Required

FINAL ANSWER

8.30259111213151 ≈ 8.302591 Meter <-- Leg Length 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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< Leg Length of Pentakis Dodecahedron Calculators

Leg Length of Pentakis Dodecahedron given Total Surface Area

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

Leg Length of Pentakis Dodecahedron given Volume

LaTeX Go Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))

Leg Length of Pentakis Dodecahedron given Midsphere Radius

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

Leg Length of Pentakis Dodecahedron

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

Leg Length of Pentakis Dodecahedron given Insphere 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 Leg Length of Pentakis Dodecahedron given Insphere Radius?

Leg Length of Pentakis Dodecahedron given Insphere Radius calculator uses Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218)))) to calculate the Leg Length of Pentakis Dodecahedron, Leg Length of Pentakis Dodecahedron given Insphere Radius formula is defined as the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron. Leg Length of Pentakis Dodecahedron is denoted by l_Leg symbol.

How to calculate Leg Length of Pentakis Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Leg Length of Pentakis Dodecahedron given Insphere Radius, enter Insphere Radius of Pentakis Dodecahedron (r_i) and hit the calculate button. Here is how the Leg Length of Pentakis Dodecahedron given Insphere Radius calculation can be explained with given input values -> 8.302591 = (3/38)*(9+sqrt(5))*((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218)))).

FAQ

What is Leg Length of Pentakis Dodecahedron given Insphere Radius?

Leg Length of Pentakis Dodecahedron given Insphere Radius formula is defined as the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron and is represented as l_Leg = (3/38)*(9+sqrt(5))*((2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218)))) or Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((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 Leg Length of Pentakis Dodecahedron given Insphere Radius?

Leg Length of Pentakis Dodecahedron given Insphere Radius formula is defined as the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron is calculated using Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218)))). To calculate Leg Length 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 Leg Length of Pentakis Dodecahedron?

In this formula, Leg Length 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 -

Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*Base Length of Pentakis Dodecahedron
Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))
Leg Length of Pentakis Dodecahedron = (3/38)*(9+sqrt(5))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))

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