Volume 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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✖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 Total Surface Area [V]

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Volume of Great Icosahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*(sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))))^3
V = (25+(9*sqrt(5)))/4*(sqrt(TSA/(3*sqrt(3)*(5+(4*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.
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

V = (25+(9*sqrt(5)))/4*(sqrt(TSA/(3*sqrt(3)*(5+(4*sqrt(5))))))^3 --> (25+(9*sqrt(5)))/4*(sqrt(7200/(3*sqrt(3)*(5+(4*sqrt(5))))))^3

Evaluating ... ...

V = 11174.6941325388

STEP 3: Convert Result to Output's Unit

11174.6941325388 Cubic Meter --> No Conversion Required

FINAL ANSWER

11174.6941325388 ≈ 11174.69 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 Total Surface Area Formula

LaTeX Go

Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*(sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))))^3
V = (25+(9*sqrt(5)))/4*(sqrt(TSA/(3*sqrt(3)*(5+(4*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 Total Surface Area?

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

How to calculate Volume of Great Icosahedron given Total Surface Area using this online calculator? To use this online calculator for Volume of Great Icosahedron given Total Surface Area, enter Total Surface Area of Great Icosahedron (TSA) and hit the calculate button. Here is how the Volume of Great Icosahedron given Total Surface Area calculation can be explained with given input values -> 11174.69 = (25+(9*sqrt(5)))/4*(sqrt(7200/(3*sqrt(3)*(5+(4*sqrt(5))))))^3.

FAQ

What is Volume of Great Icosahedron given Total Surface Area?

Volume of Great Icosahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron, calculated using total surface area and is represented as V = (25+(9*sqrt(5)))/4*(sqrt(TSA/(3*sqrt(3)*(5+(4*sqrt(5))))))^3 or Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*(sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))))^3. Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.

How to calculate Volume of Great Icosahedron given Total Surface Area?

Volume of Great Icosahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Icosahedron, calculated using total surface area is calculated using Volume of Great Icosahedron = (25+(9*sqrt(5)))/4*(sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))))^3. To calculate Volume 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 Volume of Great Icosahedron?

In this formula, Volume of Great Icosahedron uses Total Surface Area 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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