Surface to Volume Ratio of Hexakis Icosahedron given Short Edge Calculator

✖Short Edge of Hexakis Icosahedron is the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron.ⓘ Short Edge of Hexakis Icosahedron [l_e(Short)]

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✖Surface to Volume Ratio of Hexakis Icosahedron is what part of or fraction of total volume of Hexakis Icosahedron is the total surface area.ⓘ Surface to Volume Ratio of Hexakis Icosahedron given Short Edge [R_A/V]

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Formula

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Surface to Volume Ratio of Hexakis Icosahedron given Short Edge

Formula

`"R"_{"A/V"} = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*"l"_{"e(Short)"}))`

Example

`"0.223883m⁻¹"=(6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*"5m"))`

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Surface to Volume Ratio of Hexakis Icosahedron given Short Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*Short Edge of Hexakis Icosahedron))
R_A/V = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*l_e(Short)))
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 Hexakis Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Hexakis Icosahedron is what part of or fraction of total volume of Hexakis Icosahedron is the total surface area.
Short Edge of Hexakis Icosahedron - (Measured in Meter) - Short Edge of Hexakis Icosahedron is the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Short Edge of Hexakis Icosahedron: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*l_e(Short))) --> (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*5))

Evaluating ... ...

R_A/V = 0.223883158287975

STEP 3: Convert Result to Output's Unit

0.223883158287975 1 per Meter --> No Conversion Required

FINAL ANSWER

0.223883158287975 ≈ 0.223883 1 per Meter <-- Surface to Volume Ratio of Hexakis Icosahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 8 Surface to Volume Ratio of Hexakis Icosahedron Calculators

Surface to Volume Ratio of Hexakis Icosahedron given Total Surface Area

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(sqrt((15*(sqrt(10*(417+(107*sqrt(5))))))/(44*Total Surface Area of Hexakis Icosahedron)))

Surface to Volume Ratio of Hexakis Icosahedron given Insphere Radius

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((sqrt((15/241)*(275+(119*sqrt(5)))))/(4*Insphere Radius of Hexakis Icosahedron))

Surface to Volume Ratio of Hexakis Icosahedron given Volume

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(((25*(sqrt(6*(185+(82*sqrt(5))))))/(88*Volume of Hexakis Icosahedron))^(1/3))

Surface to Volume Ratio of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(5/(2*Truncated Edge of Hexakis Icosahedron*(sqrt(15*(5-sqrt(5))))))

Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*Midsphere Radius of Hexakis Icosahedron))

Surface to Volume Ratio of Hexakis Icosahedron given Medium Edge

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((3*(4+sqrt(5)))/(22*Medium Edge of Hexakis Icosahedron))

Surface to Volume Ratio of Hexakis Icosahedron given Short Edge

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*Short Edge of Hexakis Icosahedron))

Surface to Volume Ratio of Hexakis Icosahedron

Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(1/Long Edge of Hexakis Icosahedron)

Surface to Volume Ratio of Hexakis Icosahedron given Short Edge Formula

What is Hexakis Icosahedron?

A Hexakis Icosahedron is a polyhedron with identical, but irregular triangle faces. It has thirty vertices with four edges, twenty vertices with six edges and twelve vertices with ten edges.
It has 120 faces, 180 edges, 62 vertices.

How to Calculate Surface to Volume Ratio of Hexakis Icosahedron given Short Edge?

Surface to Volume Ratio of Hexakis Icosahedron given Short Edge calculator uses Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*Short Edge of Hexakis Icosahedron)) to calculate the Surface to Volume Ratio of Hexakis Icosahedron, Surface to Volume Ratio of Hexakis Icosahedron given Short Edge formula is defined as what fraction of total volume of Hexakis Icosahedron is the total surface area of Hexakis Icosahedron, calculated using short edge of Hexakis Icosahedron. Surface to Volume Ratio of Hexakis Icosahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Hexakis Icosahedron given Short Edge using this online calculator? To use this online calculator for Surface to Volume Ratio of Hexakis Icosahedron given Short Edge, enter Short Edge of Hexakis Icosahedron (l_e(Short)) and hit the calculate button. Here is how the Surface to Volume Ratio of Hexakis Icosahedron given Short Edge calculation can be explained with given input values -> 0.223883 = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*5)).

FAQ

What is Surface to Volume Ratio of Hexakis Icosahedron given Short Edge?

Surface to Volume Ratio of Hexakis Icosahedron given Short Edge formula is defined as what fraction of total volume of Hexakis Icosahedron is the total surface area of Hexakis Icosahedron, calculated using short edge of Hexakis Icosahedron and is represented as R_A/V = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*l_e(Short))) or Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*Short Edge of Hexakis Icosahedron)). Short Edge of Hexakis Icosahedron is the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron.

How to calculate Surface to Volume Ratio of Hexakis Icosahedron given Short Edge?

Surface to Volume Ratio of Hexakis Icosahedron given Short Edge formula is defined as what fraction of total volume of Hexakis Icosahedron is the total surface area of Hexakis Icosahedron, calculated using short edge of Hexakis Icosahedron is calculated using Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*Short Edge of Hexakis Icosahedron)). To calculate Surface to Volume Ratio of Hexakis Icosahedron given Short Edge, you need Short Edge of Hexakis Icosahedron (l_e(Short)). With our tool, you need to enter the respective value for Short Edge of Hexakis 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 Hexakis Icosahedron?

In this formula, Surface to Volume Ratio of Hexakis Icosahedron uses Short Edge of Hexakis Icosahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(1/Long Edge of Hexakis Icosahedron)
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((3*(4+sqrt(5)))/(22*Medium Edge of Hexakis Icosahedron))
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(5/(2*Truncated Edge of Hexakis Icosahedron*(sqrt(15*(5-sqrt(5))))))
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(sqrt((15*(sqrt(10*(417+(107*sqrt(5))))))/(44*Total Surface Area of Hexakis Icosahedron)))
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(((25*(sqrt(6*(185+(82*sqrt(5))))))/(88*Volume of Hexakis Icosahedron))^(1/3))
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*Midsphere Radius of Hexakis Icosahedron))
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((sqrt((15/241)*(275+(119*sqrt(5)))))/(4*Insphere Radius of Hexakis Icosahedron))

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