FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Face Diagonal of Dodecahedron given Insphere Radius Formula

GoFace Diagonal of Dodecahedron Formula

GoFace Diagonal of Dodecahedron given Total Surface Area Formula

Fx Copy

LaTeX Copy

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{r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

d_Face - Face Diagonal of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Face Diagonal of Dodecahedron given Insphere Radius Example

With values

With units

Only example

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

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

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

15.9839 = (1 + \sqrt{5}) \cdot \frac{11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

15.9839m = (1 + \sqrt{5}) \cdot \frac{11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

15.9839 = (1 + \sqrt{5}) \cdot \frac{11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Face Diagonal of Dodecahedron given Insphere Radius

Face Diagonal of Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

d Face = (1 + \sqrt{5}) \cdot \frac{r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Next Step Substitute values of Variables

∴

d Face = (1 + \sqrt{5}) \cdot \frac{11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Next Step Prepare to Evaluate

∴

d Face = (1 + \sqrt{5}) \cdot \frac{11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Next Step Evaluate

∴

d Face = 15.9839356161179m

LAST Step Rounding Answer

∴

d Face = 15.9839m

Face Diagonal of Dodecahedron given Insphere 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

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere 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 Total Surface Area

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

Other formulas in Face Diagonal of Dodecahedron category

Go Space Diagonal of Dodecahedron

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{l e}{2}

Go Space Diagonal of Dodecahedron given Lateral Surface Area

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

Go Space Diagonal of Dodecahedron given Perimeter

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{P}{60}

How to Evaluate Face Diagonal of Dodecahedron given Insphere Radius?

Face Diagonal of Dodecahedron given Insphere Radius evaluator uses Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10) to evaluate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Insphere Radius formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using insphere radius of Dodecahedron. Face Diagonal of Dodecahedron is denoted by d_Face symbol.

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

FAQs on Face Diagonal of Dodecahedron given Insphere Radius

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

The formula of Face Diagonal of Dodecahedron given Insphere Radius is expressed as Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10). Here is an example- 15.98394 = (1+sqrt(5))*11/sqrt((25+(11*sqrt(5)))/10).

How to calculate Face Diagonal of Dodecahedron given Insphere Radius?

With Insphere Radius of Dodecahedron (r_i) we can find Face Diagonal of Dodecahedron given Insphere Radius using the formula - Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10). 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)))))

Can the Face Diagonal of Dodecahedron given Insphere Radius be negative?

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

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

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

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit