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

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Formula

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Base Length of Pentakis Dodecahedron given Insphere Radius

Formula

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

Example

`"9.359694m"=(2*"12m")/(3*(sqrt((81+(35*sqrt(5)))/218)))`

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Base Length of Pentakis Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

Evaluating ... ...

l_Base = 9.35969364884533

STEP 3: Convert Result to Output's Unit

9.35969364884533 Meter --> No Conversion Required

FINAL ANSWER

9.35969364884533 ≈ 9.359694 Meter <-- Base Length of Pentakis Dodecahedron

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 6 Base Length of Pentakis Dodecahedron Calculators

Base Length of Pentakis Dodecahedron given Surface to Volume Ratio

Go Base Length of Pentakis Dodecahedron = ((76/19)*(sqrt(413+(162*sqrt(5)))))/(Surface to Volume Ratio of Pentakis Dodecahedron*(23+(11*sqrt(5))))

Base Length of Pentakis Dodecahedron given Total Surface Area

Go Base Length of Pentakis Dodecahedron = sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5))))))

Base Length of Pentakis Dodecahedron given Insphere Radius

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

Base Length of Pentakis Dodecahedron given Volume

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

Base Length of Pentakis Dodecahedron given Midsphere Radius

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

Base Length of Pentakis Dodecahedron given Leg Length

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

Base Length of Pentakis Dodecahedron given Insphere Radius Formula

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

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 Base Length of Pentakis Dodecahedron given Insphere Radius?

Base Length of Pentakis Dodecahedron given Insphere Radius calculator uses Base Length of Pentakis Dodecahedron = (2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))) to calculate the Base Length of Pentakis Dodecahedron, Base Length of Pentakis Dodecahedron given Insphere Radius formula is the length of the base of the isosceles triangular face of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron. Base Length of Pentakis Dodecahedron is denoted by l_Base symbol.

How to calculate Base Length of Pentakis Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Base Length of Pentakis Dodecahedron given Insphere Radius, enter Insphere Radius of Pentakis Dodecahedron (r_i) and hit the calculate button. Here is how the Base Length of Pentakis Dodecahedron given Insphere Radius calculation can be explained with given input values -> 9.359694 = (2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))).

FAQ

What is Base Length of Pentakis Dodecahedron given Insphere Radius?

Base Length of Pentakis Dodecahedron given Insphere Radius formula is the length of the base of the isosceles triangular face of Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron and is represented as l_Base = (2*r_i)/(3*(sqrt((81+(35*sqrt(5)))/218))) or Base Length of Pentakis Dodecahedron = (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 Base Length of Pentakis Dodecahedron given Insphere Radius?

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

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

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

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