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Face Diagonal of Dodecahedron given Midsphere Radius 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 = \frac{2 \cdot (1 + \sqrt{5})}{3 + \sqrt{5}} \cdot r m

d_Face - Face Diagonal of Dodecahedron?r_m - Midsphere Radius of Dodecahedron?

Face Diagonal of Dodecahedron given Midsphere Radius Example

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

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

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

16.0689 = \frac{2 \cdot (1 + \sqrt{5})}{3 + \sqrt{5}} \cdot 13

16.0689m = \frac{2 \cdot (1 + \sqrt{5})}{3 + \sqrt{5}} \cdot 13m

16.0689 = \frac{2 \cdot (1 + \sqrt{5})}{3 + \sqrt{5}} \cdot 13

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Face Diagonal of Dodecahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

d Face = \frac{2 \cdot (1 + \sqrt{5})}{3 + \sqrt{5}} \cdot r m

Next Step Substitute values of Variables

∴

d Face = \frac{2 \cdot (1 + \sqrt{5})}{3 + \sqrt{5}} \cdot 13m

Next Step Prepare to Evaluate

∴

d Face = \frac{2 \cdot (1 + \sqrt{5})}{3 + \sqrt{5}} \cdot 13

Next Step Evaluate

∴

d Face = 16.0688837074973m

LAST Step Rounding Answer

∴

d Face = 16.0689m

Face Diagonal of Dodecahedron given Midsphere Radius 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

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere Radius 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 Midsphere Radius?

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

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

FAQs on Face Diagonal of Dodecahedron given Midsphere Radius

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

The formula of Face Diagonal of Dodecahedron given Midsphere Radius is expressed as Face Diagonal of Dodecahedron = (2*(1+sqrt(5)))/(3+sqrt(5))*Midsphere Radius of Dodecahedron. Here is an example- 16.06888 = (2*(1+sqrt(5)))/(3+sqrt(5))*13.

How to calculate Face Diagonal of Dodecahedron given Midsphere Radius?

With Midsphere Radius of Dodecahedron (r_m) we can find Face Diagonal of Dodecahedron given Midsphere Radius using the formula - Face Diagonal of Dodecahedron = (2*(1+sqrt(5)))/(3+sqrt(5))*Midsphere Radius 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 Midsphere Radius be negative?

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

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

Face Diagonal of Dodecahedron given Midsphere Radius 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 Midsphere Radius can be measured.

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