Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.ⓘ Surface to Volume Ratio of Pentakis Dodecahedron [R_A/V]

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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 Surface to Volume Ratio [r_i]

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Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/R_A/V)*(sqrt((413+(162*sqrt(5))))/(23+(11*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.
Surface to Volume Ratio of Pentakis Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Pentakis Dodecahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/R_A/V)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) --> (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/0.2)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))

Evaluating ... ...

r_i = 15

STEP 3: Convert Result to Output's Unit

15 Meter --> No Conversion Required

FINAL ANSWER

15 Meter <-- Insphere Radius 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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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 Surface to Volume Ratio 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 Surface to Volume Ratio?

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio calculator uses 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)))) to calculate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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 surface to volume ratio of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Pentakis Dodecahedron (R_A/V) and hit the calculate button. Here is how the Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 15 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/0.2)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))).

FAQ

What is Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio?

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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 surface to volume ratio of the Pentakis Dodecahedron and is represented as r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/R_A/V)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) or 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)))). Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.

How to calculate Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio?

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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 surface to volume ratio of the Pentakis Dodecahedron is calculated using 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)))). To calculate Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Pentakis Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio 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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