Surface to Volume Ratio 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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✖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 given Circumsphere Radius [R_A/V]

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Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

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

Evaluating ... ...

R_A/V = 0.6396845107207

STEP 3: Convert Result to Output's Unit

0.6396845107207 1 per Meter --> No Conversion Required

FINAL ANSWER

0.6396845107207 ≈ 0.639685 1 per Meter <-- Surface to Volume Ratio of Great Icosahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

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Indian Institute of Information Technology (IIIT), Bhopal

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< Surface to Volume Ratio of Great Icosahedron Calculators

Surface to Volume Ratio of Great Icosahedron given Long Ridge Length

LaTeX Go Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(sqrt(2)*(5+(3*sqrt(5))))/(10*Long Ridge Length of Great Icosahedron)

Surface to Volume Ratio of Great Icosahedron given Mid Ridge Length

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

Surface to Volume Ratio of Great Icosahedron given Short Ridge Length

LaTeX Go Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*sqrt(10)/(5*Short Ridge Length of Great Icosahedron)

Surface to Volume Ratio of Great Icosahedron

LaTeX Go Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Edge Length of Great Icosahedron)

Surface to Volume Ratio 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 Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius?

Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius calculator uses Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(sqrt(50+(22*sqrt(5))))/(4*Circumsphere Radius of Great Icosahedron) to calculate the Surface to Volume Ratio of Great Icosahedron, Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron, calculated using circumspherer radius. Surface to Volume Ratio of Great Icosahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Great Icosahedron (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 0.639685 = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(sqrt(50+(22*sqrt(5))))/(4*25).

FAQ

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

Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron, calculated using circumspherer radius and is represented as R_A/V = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(sqrt(50+(22*sqrt(5))))/(4*r_c) or Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(sqrt(50+(22*sqrt(5))))/(4*Circumsphere Radius of Great Icosahedron). 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 Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius?

Surface to Volume Ratio of Great Icosahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron, calculated using circumspherer radius is calculated using Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(sqrt(50+(22*sqrt(5))))/(4*Circumsphere Radius of Great Icosahedron). To calculate Surface to Volume Ratio 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 Surface to Volume Ratio of Great Icosahedron?

In this formula, Surface to Volume Ratio 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 -

Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Edge Length of Great Icosahedron)
Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(1+sqrt(5))/(2*Mid Ridge Length of Great Icosahedron)
Surface to Volume Ratio of Great Icosahedron = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5))))*(sqrt(2)*(5+(3*sqrt(5))))/(10*Long Ridge Length of Great Icosahedron)

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