Surface to Volume Ratio of Great Icosahedron Calculator

✖Edge Length of Great Icosahedron is the distance between any pair of adjacent peak vertices of the Great Icosahedron.ⓘ Edge Length of Great Icosahedron [l_e]

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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 [R_A/V]

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Surface to Volume Ratio of Great Icosahedron 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)))*Edge Length of Great Icosahedron)
R_A/V = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*l_e)
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.
Edge Length of Great Icosahedron - (Measured in Meter) - Edge Length of Great Icosahedron is the distance between any pair of adjacent peak vertices of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Great Icosahedron: 10 Meter --> 10 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)))*l_e) --> (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*10)

Evaluating ... ...

R_A/V = 0.642279761591562

STEP 3: Convert Result to Output's Unit

0.642279761591562 1 per Meter --> No Conversion Required

FINAL ANSWER

0.642279761591562 ≈ 0.64228 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

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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 Formula

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)
R_A/V = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*l_e)

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?

Surface to Volume Ratio of Great Icosahedron calculator uses 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) to calculate the Surface to Volume Ratio of Great Icosahedron, Surface to Volume Ratio of Great Icosahedron formula is defined as 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 is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Great Icosahedron using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Icosahedron, enter Edge Length of Great Icosahedron (l_e) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Icosahedron calculation can be explained with given input values -> 0.64228 = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*10).

FAQ

What is Surface to Volume Ratio of Great Icosahedron?

Surface to Volume Ratio of Great Icosahedron formula is defined as the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron and is represented as R_A/V = (3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*l_e) or 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). Edge Length of Great Icosahedron is the distance between any pair of adjacent peak vertices of the Great Icosahedron.

How to calculate Surface to Volume Ratio of Great Icosahedron?

Surface to Volume Ratio of Great Icosahedron formula is defined as the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron is calculated using 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). To calculate Surface to Volume Ratio of Great Icosahedron, you need Edge Length of Great Icosahedron (l_e). With our tool, you need to enter the respective value for Edge 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 Surface to Volume Ratio of Great Icosahedron?

In this formula, Surface to Volume Ratio of Great Icosahedron uses Edge Length 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))))*(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)
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)

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