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Face Diagonal of Dodecahedron given Volume Formula

GoFace Diagonal of Dodecahedron Formula

GoFace Diagonal of Dodecahedron given Total Surface Area 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 = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

d_Face - Face Diagonal of Dodecahedron?V - Volume of Dodecahedron?

Face Diagonal of Dodecahedron given Volume Example

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

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

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

16.2063 = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

16.2063m = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

16.2063 = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

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Face Diagonal of Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Face = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d Face = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Evaluate

∴

d Face = 16.2062559218218m

LAST Step Rounding Answer

∴

d Face = 16.2063m

Face Diagonal of Dodecahedron given Volume 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

Volume of Dodecahedron

Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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 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})}}}

Go Face Diagonal of Dodecahedron given Circumsphere Radius

d Face = \frac{2}{\sqrt{3}} \cdot r c

How to Evaluate Face Diagonal of Dodecahedron given Volume?

Face Diagonal of Dodecahedron given Volume evaluator uses Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3) to evaluate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Volume formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using volume of Dodecahedron. Face Diagonal of Dodecahedron is denoted by d_Face symbol.

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

FAQs on Face Diagonal of Dodecahedron given Volume

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

The formula of Face Diagonal of Dodecahedron given Volume is expressed as Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). Here is an example- 16.20626 = (1+sqrt(5))/2*((4*7700)/(15+(7*sqrt(5))))^(1/3).

How to calculate Face Diagonal of Dodecahedron given Volume?

With Volume of Dodecahedron (V) we can find Face Diagonal of Dodecahedron given Volume using the formula - Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). 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*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron=(1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))

Can the Face Diagonal of Dodecahedron given Volume be negative?

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

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

Face Diagonal of Dodecahedron given Volume 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 Volume can be measured.

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