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Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Formula

GoLong Edge of Pentagonal Hexecontahedron Formula

GoLong Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Formula

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Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron. Check FAQs

l e(Long) = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{AV \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi]))}{31}

l_e(Long) - Long Edge of Pentagonal Hexecontahedron?AV - SA:V of Pentagonal Hexecontahedron?[phi] - Golden ratio?[phi] - Golden ratio?[phi] - Golden ratio?

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Example

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Here is how the Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio equation looks like with Values.

Here is how the Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio equation looks like with Units.

Here is how the Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio equation looks like.

5.8609 = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{0.2 \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot 1.618 + 2) + (5 \cdot 1.618 - 3) + 2 \cdot (8 - 3 \cdot 1.618))}{31}

5.8609m = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{0.2m⁻¹ \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot 1.618 + 2) + (5 \cdot 1.618 - 3) + 2 \cdot (8 - 3 \cdot 1.618))}{31}

5.8609 = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{0.2 \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot 1.618 + 2) + (5 \cdot 1.618 - 3) + 2 \cdot (8 - 3 \cdot 1.618))}{31}

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Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

FIRST Step Consider the formula

l e(Long) = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{AV \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi]))}{31}

Next Step Substitute values of Variables

∴

l e(Long) = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{0.2m⁻¹ \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi]))}{31}

Next Step Substitute values of Constants

∴

l e(Long) = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{0.2m⁻¹ \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot 1.618 + 2) + (5 \cdot 1.618 - 3) + 2 \cdot (8 - 3 \cdot 1.618))}{31}

Next Step Prepare to Evaluate

∴

l e(Long) = (\frac{6 \cdot (2 + 3 \cdot 0.4715756) \cdot \frac{\sqrt{1 - {0.4715756}^{2}}}{1 - 2 \cdot {0.4715756}^{2}}}{0.2 \cdot \frac{(1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)}{(1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot 1.618 + 2) + (5 \cdot 1.618 - 3) + 2 \cdot (8 - 3 \cdot 1.618))}{31}

Next Step Evaluate

∴

l e(Long) = 5.8609473259107m

LAST Step Rounding Answer

∴

l e(Long) = 5.8609m

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Formula Elements

Variables

Constants

Functions

Long Edge of Pentagonal Hexecontahedron

Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron.

Symbol: l_e(Long)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Edge of Pentagonal Hexecontahedron

SA:V of Pentagonal Hexecontahedron

SA:V of Pentagonal Hexecontahedron is what part of or fraction of total volume of Pentagonal Hexecontahedron is the total surface area.

Symbol: AV

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find SA:V of Pentagonal Hexecontahedron

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

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.

Syntax: sqrt(Number)

Other Formulas to find Long Edge of Pentagonal Hexecontahedron

Go Long Edge of Pentagonal Hexecontahedron

l e(Long) = (l e(Short) \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi]))}{31}

Go Long Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

l e(Long) = (\frac{l e(Snub Dodecahedron)}{\sqrt{2 + 2 \cdot (0.4715756)}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi]))}{31}

Go Long Edge of Pentagonal Hexecontahedron given Total Surface Area

l e(Long) = (\sqrt{\frac{TSA \cdot (1 - 2 \cdot {0.4715756}^{2})}{30 \cdot (2 + 3 \cdot 0.4715756) \cdot \sqrt{1 - {0.4715756}^{2}}}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi]))}{31}

Go Long Edge of Pentagonal Hexecontahedron given Volume

l e(Long) = ({(\frac{V \cdot (1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}{5 \cdot (1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)})}^{\frac{1}{3}} \cdot \sqrt{2 + 2 \cdot 0.4715756}) \cdot \frac{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi]))}{31}

How to Evaluate Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio evaluator uses Long Edge of Pentagonal Hexecontahedron = ((6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31 to evaluate the Long Edge of Pentagonal Hexecontahedron, Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio formula is defined as the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron, calculated using surface to volume ratio of Pentagonal Hexecontahedron. Long Edge of Pentagonal Hexecontahedron is denoted by l_e(Long) symbol.

How to evaluate Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio, enter SA:V of Pentagonal Hexecontahedron (AV) and hit the calculate button.

FAQs on Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio

What is the formula to find Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

The formula of Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio is expressed as Long Edge of Pentagonal Hexecontahedron = ((6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31. Here is an example- 5.860947 = ((6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(0.2*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31.

How to calculate Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

With SA:V of Pentagonal Hexecontahedron (AV) we can find Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio using the formula - Long Edge of Pentagonal Hexecontahedron = ((6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31. This formula also uses Golden ratio, Golden ratio, Golden ratio constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Long Edge of Pentagonal Hexecontahedron?

Here are the different ways to Calculate Long Edge of Pentagonal Hexecontahedron-

Long Edge of Pentagonal Hexecontahedron=(Short Edge of Pentagonal Hexecontahedron*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
Long Edge of Pentagonal Hexecontahedron=(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31
Long Edge of Pentagonal Hexecontahedron=(sqrt((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))*sqrt(2+2*0.4715756))*(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi])))/31

Can the Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio be negative?

No, the Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio, measured in Length cannot be negative.

Which unit is used to measure Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio can be measured.

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Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Formula

​GoLong Edge of Pentagonal Hexecontahedron Formula

​GoLong Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Formula

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Example

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Solution

Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Formula Elements

Other Formulas to find Long Edge of Pentagonal Hexecontahedron

How to Evaluate Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

FAQs on Long Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio

Variable Name

GoLong Edge of Pentagonal Hexecontahedron Formula

GoLong Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Formula