Circumsphere Radius of Great Icosahedron given Volume Calculator

✖Volume of Great Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron.ⓘ Volume of Great Icosahedron [V]

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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 Volume [r_c]

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Circumsphere Radius of Great Icosahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)
r_c = sqrt(50+(22*sqrt(5)))/4*((4*V)/(25+(9*sqrt(5))))^(1/3)
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.
Volume of Great Icosahedron - (Measured in Cubic Meter) - Volume of Great Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Great Icosahedron: 11000 Cubic Meter --> 11000 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(50+(22*sqrt(5)))/4*((4*V)/(25+(9*sqrt(5))))^(1/3) --> sqrt(50+(22*sqrt(5)))/4*((4*11000)/(25+(9*sqrt(5))))^(1/3)

Evaluating ... ...

r_c = 24.6903931471964

STEP 3: Convert Result to Output's Unit

24.6903931471964 Meter --> No Conversion Required

FINAL ANSWER

24.6903931471964 ≈ 24.69039 Meter <-- Circumsphere Radius of Great Icosahedron

(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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< Radius of Great Icosahedron Calculators

Circumsphere Radius of Great Icosahedron given Long Ridge Length

LaTeX 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 Mid Ridge Length

LaTeX 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

LaTeX 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

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

Circumsphere Radius of Great Icosahedron given Volume Formula

LaTeX Go

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

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 Volume?

Circumsphere Radius of Great Icosahedron given Volume calculator uses Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3) to calculate the Circumsphere Radius of Great Icosahedron, Circumsphere Radius of Great Icosahedron given Volume 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 volume. Circumsphere Radius of Great Icosahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Icosahedron given Volume using this online calculator? To use this online calculator for Circumsphere Radius of Great Icosahedron given Volume, enter Volume of Great Icosahedron (V) and hit the calculate button. Here is how the Circumsphere Radius of Great Icosahedron given Volume calculation can be explained with given input values -> 24.69039 = sqrt(50+(22*sqrt(5)))/4*((4*11000)/(25+(9*sqrt(5))))^(1/3).

FAQ

What is Circumsphere Radius of Great Icosahedron given Volume?

Circumsphere Radius of Great Icosahedron given Volume 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 volume and is represented as r_c = sqrt(50+(22*sqrt(5)))/4*((4*V)/(25+(9*sqrt(5))))^(1/3) or Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3). Volume of Great Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron.

How to calculate Circumsphere Radius of Great Icosahedron given Volume?

Circumsphere Radius of Great Icosahedron given Volume 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 volume is calculated using Circumsphere Radius of Great Icosahedron = sqrt(50+(22*sqrt(5)))/4*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3). To calculate Circumsphere Radius of Great Icosahedron given Volume, you need Volume of Great Icosahedron (V). With our tool, you need to enter the respective value for Volume 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 Volume of Great Icosahedron. We can use 3 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))))

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