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Face Diagonal of Dodecahedron given Surface to Volume Ratio Formula

GoFace Diagonal of Dodecahedron Formula

GoFace Diagonal of Dodecahedron given Volume Formula

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The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron. Check FAQs

d Face = (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{(15 + (7 \cdot \sqrt{5})) \cdot R A/V}

d_Face - Face Diagonal of Dodecahedron?R_A/V - Surface to Volume Ratio of Dodecahedron?

Face Diagonal of Dodecahedron given Surface to Volume Ratio Example

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Here is how the Face Diagonal of Dodecahedron given Surface to Volume Ratio equation looks like with Values.

Here is how the Face Diagonal of Dodecahedron given Surface to Volume Ratio equation looks like with Units.

Here is how the Face Diagonal of Dodecahedron given Surface to Volume Ratio equation looks like.

14.5309 = (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{(15 + (7 \cdot \sqrt{5})) \cdot 0.3}

14.5309m = (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{(15 + (7 \cdot \sqrt{5})) \cdot 0.3m⁻¹}

14.5309 = (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{(15 + (7 \cdot \sqrt{5})) \cdot 0.3}

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Face Diagonal of Dodecahedron given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Face Diagonal of Dodecahedron given Surface to Volume Ratio?

FIRST Step Consider the formula

d Face = (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{(15 + (7 \cdot \sqrt{5})) \cdot R A/V}

Next Step Substitute values of Variables

∴

d Face = (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{(15 + (7 \cdot \sqrt{5})) \cdot 0.3m⁻¹}

Next Step Prepare to Evaluate

∴

d Face = (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{(15 + (7 \cdot \sqrt{5})) \cdot 0.3}

Next Step Evaluate

∴

d Face = 14.5308505601072m

LAST Step Rounding Answer

∴

d Face = 14.5309m

Face Diagonal of Dodecahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Face Diagonal of Dodecahedron

The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.

Symbol: d_Face

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Face Diagonal of Dodecahedron

Surface to Volume Ratio of Dodecahedron

The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Dodecahedron

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 Face Diagonal of Dodecahedron

Go Face Diagonal of Dodecahedron

d Face = (\frac{1 + \sqrt{5}}{2}) \cdot l e

Go Face Diagonal of Dodecahedron given Volume

d Face = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Face Diagonal of Dodecahedron given Total Surface Area

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Face Diagonal of Dodecahedron given Face Area

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Face Diagonal of Dodecahedron given Surface to Volume Ratio?

Face Diagonal of Dodecahedron given Surface to Volume Ratio evaluator uses Face Diagonal of Dodecahedron = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Surface to Volume Ratio of Dodecahedron) to evaluate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Surface to Volume Ratio formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using surface to volume ratio of Dodecahedron. Face Diagonal of Dodecahedron is denoted by d_Face symbol.

How to evaluate Face Diagonal of Dodecahedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Face Diagonal of Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Dodecahedron (R_A/V) and hit the calculate button.

FAQs on Face Diagonal of Dodecahedron given Surface to Volume Ratio

What is the formula to find Face Diagonal of Dodecahedron given Surface to Volume Ratio?

The formula of Face Diagonal of Dodecahedron given Surface to Volume Ratio is expressed as Face Diagonal of Dodecahedron = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Surface to Volume Ratio of Dodecahedron). Here is an example- 14.53085 = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*0.3).

How to calculate Face Diagonal of Dodecahedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Dodecahedron (R_A/V) we can find Face Diagonal of Dodecahedron given Surface to Volume Ratio using the formula - Face Diagonal of Dodecahedron = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Surface to Volume Ratio of Dodecahedron). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Face Diagonal of Dodecahedron?

Here are the different ways to Calculate Face Diagonal of Dodecahedron-

Face Diagonal of Dodecahedron=((1+sqrt(5))/2)*Edge Length of Dodecahedron
Face Diagonal of Dodecahedron=(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Face Diagonal of Dodecahedron=(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

Can the Face Diagonal of Dodecahedron given Surface to Volume Ratio be negative?

No, the Face Diagonal of Dodecahedron given Surface to Volume Ratio, measured in Length cannot be negative.

Which unit is used to measure Face Diagonal of Dodecahedron given Surface to Volume Ratio?

Face Diagonal of Dodecahedron 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 Face Diagonal of Dodecahedron given Surface to Volume Ratio can be measured.

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