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Midsphere Radius of Dodecahedron given Face Diagonal Formula

GoMidsphere Radius of Dodecahedron Formula

GoMidsphere Radius of Dodecahedron given Volume Formula

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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. Check FAQs

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

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

Midsphere Radius of Dodecahedron given Face Diagonal Example

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

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

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

12.9443 = \frac{3 + \sqrt{5}}{2} \cdot \frac{16}{1 + \sqrt{5}}

12.9443m = \frac{3 + \sqrt{5}}{2} \cdot \frac{16m}{1 + \sqrt{5}}

12.9443 = \frac{3 + \sqrt{5}}{2} \cdot \frac{16}{1 + \sqrt{5}}

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Midsphere Radius of Dodecahedron given Face Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r m = \frac{3 + \sqrt{5}}{2} \cdot \frac{16m}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

r m = \frac{3 + \sqrt{5}}{2} \cdot \frac{16}{1 + \sqrt{5}}

Next Step Evaluate

∴

r m = 12.9442719099992m

LAST Step Rounding Answer

∴

r m = 12.9443m

Midsphere Radius of Dodecahedron given Face Diagonal Formula Elements

Variables

Functions

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

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 Midsphere Radius of Dodecahedron

Go Midsphere Radius of Dodecahedron

r m = \frac{3 + \sqrt{5}}{4} \cdot l e

Go Midsphere Radius of Dodecahedron given Volume

r m = \frac{3 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Midsphere Radius of Dodecahedron given Total Surface Area

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Midsphere Radius of Dodecahedron given Face Area

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Midsphere Radius of Dodecahedron given Face Diagonal?

Midsphere Radius of Dodecahedron given Face Diagonal evaluator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Face Diagonal of Dodecahedron/(1+sqrt(5)) to evaluate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron given Face Diagonal formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using face diagonal of Dodecahedron. Midsphere Radius of Dodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Dodecahedron given Face Diagonal

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

The formula of Midsphere Radius of Dodecahedron given Face Diagonal is expressed as Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Face Diagonal of Dodecahedron/(1+sqrt(5)). Here is an example- 12.94427 = (3+sqrt(5))/2*16/(1+sqrt(5)).

How to calculate Midsphere Radius of Dodecahedron given Face Diagonal?

With Face Diagonal of Dodecahedron (d_Face) we can find Midsphere Radius of Dodecahedron given Face Diagonal using the formula - Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Face Diagonal of Dodecahedron/(1+sqrt(5)). This formula also uses Square Root (sqrt) function(s).

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

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

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

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

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

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

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

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