Mid Ridge Length 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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✖Mid Ridge Length of Great Icosahedron the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached.ⓘ Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio [l_Ridge(Mid)]

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Formula

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Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio

Formula

`"l"_{"Ridge(Mid)"} = (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*"R"_{"A/V"})`

Example

`"17.32051m"=(1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*"0.6m⁻¹")`

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Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Mid Ridge Length of Great Icosahedron - (Measured in Meter) - Mid Ridge Length of Great Icosahedron the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached.
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

l_Ridge(Mid) = (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V) --> (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6)

Evaluating ... ...

l_Ridge(Mid) = 17.3205080756888

STEP 3: Convert Result to Output's Unit

17.3205080756888 Meter --> No Conversion Required

FINAL ANSWER

17.3205080756888 ≈ 17.32051 Meter <-- Mid Ridge Length 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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< 7 Mid Ridge Length of Great Icosahedron Calculators

Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio

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

Mid Ridge Length of Great Icosahedron given Total Surface Area

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

Mid Ridge Length of Great Icosahedron given Long Ridge Length

Go Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))

Mid Ridge Length of Great Icosahedron given Circumsphere Radius

Go Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(4*Circumsphere Radius of Great Icosahedron)/sqrt(50+(22*sqrt(5)))

Mid Ridge Length of Great Icosahedron given Volume

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

Mid Ridge Length of Great Icosahedron given Short Ridge Length

Go Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)

Mid Ridge Length of Great Icosahedron

Go Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*Edge Length of Great Icosahedron

Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio Formula

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 Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio?

Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio calculator uses Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron) to calculate the Mid Ridge Length of Great Icosahedron, Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio formula is defined as the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached, calculated using surface to volume ratio. Mid Ridge Length of Great Icosahedron is denoted by l_Ridge(Mid) symbol.

How to calculate Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Mid Ridge Length 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 Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 17.32051 = (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6).

FAQ

What is Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio?

Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio formula is defined as the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached, calculated using surface to volume ratio and is represented as l_Ridge(Mid) = (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V) or Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron). 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 Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio?

Mid Ridge Length of Great Icosahedron given Surface to Volume Ratio formula is defined as the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached, calculated using surface to volume ratio is calculated using Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron). To calculate Mid Ridge Length 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 Mid Ridge Length of Great Icosahedron?

In this formula, Mid Ridge Length of Great Icosahedron uses Surface to Volume Ratio of Great Icosahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*Edge Length of Great Icosahedron
Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5))))
Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)
Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*(4*Circumsphere Radius of Great Icosahedron)/sqrt(50+(22*sqrt(5)))
Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5)))))
Mid Ridge Length of Great Icosahedron = (1+sqrt(5))/2*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)

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