Volume of Great Icosahedron given Long Ridge Length Calculator

✖Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.ⓘ Long Ridge Length of Great Icosahedron [l_Ridge(Long)]

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

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Volume of Great Icosahedron given Long Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^3
V = (25+(9*sqrt(5)))/4*((10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))))^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

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.
Long Ridge Length of Great Icosahedron - (Measured in Meter) - Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.

STEP 1: Convert Input(s) to Base Unit

Long Ridge Length of Great Icosahedron: 17 Meter --> 17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (25+(9*sqrt(5)))/4*((10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))))^3 --> (25+(9*sqrt(5)))/4*((10*17)/(sqrt(2)*(5+(3*sqrt(5)))))^3

Evaluating ... ...

V = 12209.1217075374

STEP 3: Convert Result to Output's Unit

12209.1217075374 Cubic Meter --> No Conversion Required

FINAL ANSWER

12209.1217075374 ≈ 12209.12 Cubic Meter <-- Volume of Great Icosahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Volume of Great Icosahedron Calculators

Volume of Great Icosahedron given Long Ridge Length

LaTeX Go Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^3

Volume of Great Icosahedron given Mid Ridge Length

LaTeX Go Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^3

Volume of Great Icosahedron given Short Ridge Length

LaTeX Go Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((5*Short Ridge Length of Great Icosahedron)/sqrt(10))^3

Volume of Great Icosahedron

LaTeX Go Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*Edge Length of Great Icosahedron^3

Volume of Great Icosahedron given Long Ridge Length Formula

LaTeX Go

Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^3
V = (25+(9*sqrt(5)))/4*((10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))))^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 Volume of Great Icosahedron given Long Ridge Length?

Volume of Great Icosahedron given Long Ridge Length calculator uses Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^3 to calculate the Volume of Great Icosahedron, Volume of Great Icosahedron given Long Ridge Length formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Icosahedron, calculated using long ridge length. Volume of Great Icosahedron is denoted by V symbol.

How to calculate Volume of Great Icosahedron given Long Ridge Length using this online calculator? To use this online calculator for Volume of Great Icosahedron given Long Ridge Length, enter Long Ridge Length of Great Icosahedron (l_Ridge(Long)) and hit the calculate button. Here is how the Volume of Great Icosahedron given Long Ridge Length calculation can be explained with given input values -> 12209.12 = (25+(9*sqrt(5)))/4*((10*17)/(sqrt(2)*(5+(3*sqrt(5)))))^3.

FAQ

What is Volume of Great Icosahedron given Long Ridge Length?

Volume of Great Icosahedron given Long Ridge Length formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Icosahedron, calculated using long ridge length and is represented as V = (25+(9*sqrt(5)))/4*((10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))))^3 or Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^3. Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.

How to calculate Volume of Great Icosahedron given Long Ridge Length?

Volume of Great Icosahedron given Long Ridge Length formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Icosahedron, calculated using long ridge length is calculated using Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^3. To calculate Volume of Great Icosahedron given Long Ridge Length, you need Long Ridge Length of Great Icosahedron (l_Ridge(Long)). With our tool, you need to enter the respective value for Long Ridge Length 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 Volume of Great Icosahedron?

In this formula, Volume of Great Icosahedron uses Long Ridge Length of Great Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*Edge Length of Great Icosahedron^3
Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^3
Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((5*Short Ridge Length of Great Icosahedron)/sqrt(10))^3

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