Circumsphere Radius of Great Icosahedron given Total Surface Area Calculator

✖Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.ⓘ Total Surface Area of Great Icosahedron [TSA]

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✖Circumsphere Radius of Great Icosahedron is the radius of the sphere that contains the Great Icosahedron in such a way that all the peak vertices are lying on the sphere.ⓘ Circumsphere Radius of Great Icosahedron given Total Surface Area [r_c]

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Formula

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Circumsphere Radius of Great Icosahedron given Total Surface Area

Formula

`"r"_{"c"} = sqrt(50+(22*sqrt(5)))/4*sqrt("TSA"/(3*sqrt(3)*(5+(4*sqrt(5)))))`

Example

`"24.82041m"=sqrt(50+(22*sqrt(5)))/4*sqrt("7200m²"/(3*sqrt(3)*(5+(4*sqrt(5)))))`

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Circumsphere Radius of Great Icosahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5)))))
r_c = sqrt(50+(22*sqrt(5)))/4*sqrt(TSA/(3*sqrt(3)*(5+(4*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

Circumsphere Radius of Great Icosahedron - (Measured in Meter) - Circumsphere Radius of Great Icosahedron is the radius of the sphere that contains the Great Icosahedron in such a way that all the peak vertices are lying on the sphere.
Total Surface Area of Great Icosahedron - (Measured in Square Meter) - Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Great Icosahedron: 7200 Square Meter --> 7200 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(50+(22*sqrt(5)))/4*sqrt(TSA/(3*sqrt(3)*(5+(4*sqrt(5))))) --> sqrt(50+(22*sqrt(5)))/4*sqrt(7200/(3*sqrt(3)*(5+(4*sqrt(5)))))

Evaluating ... ...

r_c = 24.8204123216201

STEP 3: Convert Result to Output's Unit

24.8204123216201 Meter --> No Conversion Required

FINAL ANSWER

24.8204123216201 ≈ 24.82041 Meter <-- Circumsphere Radius of Great Icosahedron

(Calculation completed in 00.004 seconds)

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Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< 7 Radius of Great Icosahedron Calculators

Circumsphere Radius of Great Icosahedron given Surface to Volume Ratio

Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron)

Circumsphere Radius of Great Icosahedron given Total Surface Area

Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5)))))

Circumsphere Radius of Great Icosahedron given Long Ridge Length

Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))

Circumsphere Radius of Great Icosahedron given Volume

Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)

Circumsphere Radius of Great Icosahedron given Mid Ridge Length

Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5))

Circumsphere Radius of Great Icosahedron given Short Ridge Length

Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)

Circumsphere Radius of Great Icosahedron

Go Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*Edge Length of Great Icosahedron

Circumsphere Radius of Great Icosahedron given Total Surface Area Formula

What is Great Icosahedron?

The Great Icosahedron can be constructed from an icosahedron with unit edge lengths by taking the 20 sets of vertices that are mutually spaced by a distance phi, the golden ratio. The solid therefore consists of 20 equilateral triangles. The symmetry of their arrangement is such that the resulting solid contains 12 pentagrams.

How to Calculate Circumsphere Radius of Great Icosahedron given Total Surface Area?

Circumsphere Radius of Great Icosahedron given Total Surface Area calculator uses Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))) to calculate the Circumsphere Radius of Great Icosahedron, Circumsphere Radius of Great Icosahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Great Icosahedron in such a way that all the vertices are lying on the sphere, calculated using total surface area. Circumsphere Radius of Great Icosahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Icosahedron given Total Surface Area using this online calculator? To use this online calculator for Circumsphere Radius of Great Icosahedron given Total Surface Area, enter Total Surface Area of Great Icosahedron (TSA) and hit the calculate button. Here is how the Circumsphere Radius of Great Icosahedron given Total Surface Area calculation can be explained with given input values -> 24.82041 = sqrt(50+(22*sqrt(5)))/4*sqrt(7200/(3*sqrt(3)*(5+(4*sqrt(5))))).

FAQ

What is Circumsphere Radius of Great Icosahedron given Total Surface Area?

Circumsphere Radius of Great Icosahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Great Icosahedron in such a way that all the vertices are lying on the sphere, calculated using total surface area and is represented as r_c = sqrt(50+(22*sqrt(5)))/4*sqrt(TSA/(3*sqrt(3)*(5+(4*sqrt(5))))) or Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))). Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.

How to calculate Circumsphere Radius of Great Icosahedron given Total Surface Area?

Circumsphere Radius of Great Icosahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Great Icosahedron in such a way that all the vertices are lying on the sphere, calculated using total surface area is calculated using Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))). To calculate Circumsphere Radius of Great Icosahedron given Total Surface Area, you need Total Surface Area of Great Icosahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Great Icosahedron 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 Circumsphere Radius of Great Icosahedron?

In this formula, Circumsphere Radius of Great Icosahedron uses Total Surface Area of Great Icosahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*Edge Length of Great Icosahedron
Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5))
Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))
Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)
Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)
Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron)

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