Total Surface Area of Great Icosahedron given Circumsphere Radius Calculator

✖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 [r_c]

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✖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 given Circumsphere Radius [TSA]

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Total Surface Area of Great Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))))^2
TSA = 3*sqrt(3)*(5+4*sqrt(5))*((4*r_c)/(sqrt(50+(22*sqrt(5)))))^2
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Great Icosahedron: 25 Meter --> 25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 3*sqrt(3)*(5+4*sqrt(5))*((4*r_c)/(sqrt(50+(22*sqrt(5)))))^2 --> 3*sqrt(3)*(5+4*sqrt(5))*((4*25)/(sqrt(50+(22*sqrt(5)))))^2

Evaluating ... ...

TSA = 7304.56789521781

STEP 3: Convert Result to Output's Unit

7304.56789521781 Square Meter --> No Conversion Required

FINAL ANSWER

7304.56789521781 ≈ 7304.568 Square Meter <-- Total Surface Area of Great Icosahedron

(Calculation completed in 00.004 seconds)

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< Total Surface Area of Great Icosahedron Calculators

Total Surface Area of Great Icosahedron given Long Ridge Length

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2

Total Surface Area of Great Icosahedron given Mid Ridge Length

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^2

Total Surface Area of Great Icosahedron given Short Ridge Length

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((5*Short Ridge Length of Great Icosahedron)/sqrt(10))^2

Total Surface Area of Great Icosahedron

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*Edge Length of Great Icosahedron^2

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

Total Surface Area of Great Icosahedron given Circumsphere Radius calculator uses Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))))^2 to calculate the Total Surface Area of Great Icosahedron, Total Surface Area of Great Icosahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using circumsphere radius. Total Surface Area of Great Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Great Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Great Icosahedron (r_c) and hit the calculate button. Here is how the Total Surface Area of Great Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 7304.568 = 3*sqrt(3)*(5+4*sqrt(5))*((4*25)/(sqrt(50+(22*sqrt(5)))))^2.

FAQ

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

Total Surface Area of Great Icosahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using circumsphere radius and is represented as TSA = 3*sqrt(3)*(5+4*sqrt(5))*((4*r_c)/(sqrt(50+(22*sqrt(5)))))^2 or Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))))^2. 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.

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

Total Surface Area of Great Icosahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using circumsphere radius is calculated using Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))))^2. To calculate Total Surface Area of Great Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Great Icosahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Total Surface Area of Great Icosahedron?

In this formula, Total Surface Area of Great Icosahedron uses Circumsphere Radius of Great Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*Edge Length of Great Icosahedron^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2

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