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Insphere Radius of Dodecahedron given Face Diagonal Formula

GoInsphere Radius of Dodecahedron Formula

GoInsphere Radius of Dodecahedron given Volume Formula

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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. Check FAQs

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

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

Insphere Radius of Dodecahedron given Face Diagonal Example

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

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

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

11.0111 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{16}{1 + \sqrt{5}}

11.0111m = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{16m}{1 + \sqrt{5}}

11.0111 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{16}{1 + \sqrt{5}}

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Insphere Radius of Dodecahedron given Face Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{16m}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{16}{1 + \sqrt{5}}

Next Step Evaluate

∴

r i = 11.0110553637694m

LAST Step Rounding Answer

∴

r i = 11.0111m

Insphere Radius of Dodecahedron given Face Diagonal Formula Elements

Variables

Functions

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

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

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 Insphere Radius of Dodecahedron

Go Insphere Radius of Dodecahedron

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{l e}{2}

Go Insphere Radius of Dodecahedron given Volume

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Insphere Radius of Dodecahedron given Total Surface Area

r i = \sqrt{\frac{TSA \cdot (25 + (11 \cdot \sqrt{5}))}{120 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Insphere Radius of Dodecahedron given Face Area

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

How to Evaluate Insphere Radius of Dodecahedron given Face Diagonal?

Insphere Radius of Dodecahedron given Face Diagonal evaluator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Face Diagonal of Dodecahedron/(1+sqrt(5)) to evaluate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Face Diagonal formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using face diagonal of Dodecahedron. Insphere Radius of Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Dodecahedron given Face Diagonal

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

The formula of Insphere Radius of Dodecahedron given Face Diagonal is expressed as Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Face Diagonal of Dodecahedron/(1+sqrt(5)). Here is an example- 11.01106 = sqrt((25+(11*sqrt(5)))/10)*16/(1+sqrt(5)).

How to calculate Insphere Radius of Dodecahedron given Face Diagonal?

With Face Diagonal of Dodecahedron (d_Face) we can find Insphere Radius of Dodecahedron given Face Diagonal using the formula - Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Face Diagonal of Dodecahedron/(1+sqrt(5)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Insphere Radius of Dodecahedron?

Here are the different ways to Calculate Insphere Radius of Dodecahedron-

Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Insphere Radius of Dodecahedron=sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))

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

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

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

Insphere Radius of Dodecahedron given Face Diagonal is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Insphere Radius of Dodecahedron given Face Diagonal can be measured.

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