Volume of Great Icosahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.ⓘ Surface to Volume Ratio of Great Icosahedron [R_A/V]

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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 Surface to Volume Ratio [V]

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Volume of Great Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^3
V = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V))^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.
Surface to Volume Ratio of Great Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Great Icosahedron: 0.6 1 per Meter --> 0.6 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V))^3 --> (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6))^3

Evaluating ... ...

V = 13837.9720392057

STEP 3: Convert Result to Output's Unit

13837.9720392057 Cubic Meter --> No Conversion Required

FINAL ANSWER

13837.9720392057 ≈ 13837.97 Cubic Meter <-- Volume 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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< 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 Surface to Volume Ratio Formula

LaTeX Go

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 Surface to Volume Ratio?

Volume of Great Icosahedron given Surface to Volume Ratio calculator uses Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^3 to calculate the Volume of Great Icosahedron, Volume of Great Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron, calculated using surface to volume ratio. Volume of Great Icosahedron is denoted by V symbol.

How to calculate Volume of Great Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Great Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Great Icosahedron (R_A/V) and hit the calculate button. Here is how the Volume of Great Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 13837.97 = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6))^3.

FAQ

What is Volume of Great Icosahedron given Surface to Volume Ratio?

Volume of Great Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron, calculated using surface to volume ratio and is represented as V = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V))^3 or Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^3. Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.

How to calculate Volume of Great Icosahedron given Surface to Volume Ratio?

Volume of Great Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron, calculated using surface to volume ratio is calculated using Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^3. To calculate Volume of Great Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Great Icosahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio 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*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^3

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