Insphere Radius of Pentakis Dodecahedron given Total Surface Area Calculator

✖Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.ⓘ Total Surface Area of Pentakis Dodecahedron [TSA]

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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 Total Surface Area [r_i]

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Insphere Radius of Pentakis Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))))))
r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*TSA)/(15*(sqrt(413+(162*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.
Total Surface Area of Pentakis Dodecahedron - (Measured in Square Meter) - Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Pentakis Dodecahedron: 2200 Square Meter --> 2200 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*TSA)/(15*(sqrt(413+(162*sqrt(5))))))) --> (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*2200)/(15*(sqrt(413+(162*sqrt(5)))))))

Evaluating ... ...

r_i = 12.8263373475288

STEP 3: Convert Result to Output's Unit

12.8263373475288 Meter --> No Conversion Required

FINAL ANSWER

12.8263373475288 ≈ 12.82634 Meter <-- Insphere Radius 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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< 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 Total Surface Area 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 Total Surface Area?

Insphere Radius of Pentakis Dodecahedron given Total Surface Area calculator uses 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))))))) to calculate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Total Surface Area 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 total surface area of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Pentakis Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Insphere Radius of Pentakis Dodecahedron given Total Surface Area, enter Total Surface Area of Pentakis Dodecahedron (TSA) and hit the calculate button. Here is how the Insphere Radius of Pentakis Dodecahedron given Total Surface Area calculation can be explained with given input values -> 12.82634 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*2200)/(15*(sqrt(413+(162*sqrt(5))))))).

FAQ

What is Insphere Radius of Pentakis Dodecahedron given Total Surface Area?

Insphere Radius of Pentakis Dodecahedron given Total Surface Area 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 total surface area of the Pentakis Dodecahedron and is represented as r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*TSA)/(15*(sqrt(413+(162*sqrt(5))))))) or 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))))))). Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.

How to calculate Insphere Radius of Pentakis Dodecahedron given Total Surface Area?

Insphere Radius of Pentakis Dodecahedron given Total Surface Area 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 total surface area of the Pentakis Dodecahedron is calculated using 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))))))). To calculate Insphere Radius of Pentakis Dodecahedron given Total Surface Area, you need Total Surface Area of Pentakis Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Total Surface Area 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))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))

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