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Circumsphere Radius of Dodecahedron given Face Diagonal Formula

GoCircumsphere Radius of Dodecahedron Formula

GoCircumsphere Radius of Dodecahedron given Volume Formula

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Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere. Check FAQs

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

r_c - Circumsphere Radius of Dodecahedron?d_Face - Face Diagonal of Dodecahedron?

Circumsphere Radius of Dodecahedron given Face Diagonal Example

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

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

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

13.8564 = \frac{\sqrt{3}}{2} \cdot 16

13.8564m = \frac{\sqrt{3}}{2} \cdot 16m

13.8564 = \frac{\sqrt{3}}{2} \cdot 16

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Circumsphere Radius of Dodecahedron given Face Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{3}}{2} \cdot 16m

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{3}}{2} \cdot 16

Next Step Evaluate

∴

r c = 13.856406460551m

LAST Step Rounding Answer

∴

r c = 13.8564m

Circumsphere Radius of Dodecahedron given Face Diagonal Formula Elements

Variables

Functions

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere 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 Circumsphere Radius of Dodecahedron

Go Circumsphere Radius of Dodecahedron

r c = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{l e}{4}

Go Circumsphere Radius of Dodecahedron given Volume

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

Go Circumsphere Radius of Dodecahedron given Total Surface Area

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Circumsphere Radius of Dodecahedron given Face Area

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Circumsphere Radius of Dodecahedron given Face Diagonal?

Circumsphere Radius of Dodecahedron given Face Diagonal evaluator uses Circumsphere Radius of Dodecahedron = sqrt(3)/2*Face Diagonal of Dodecahedron to evaluate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Face Diagonal formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using face diagonal of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Dodecahedron given Face Diagonal

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

The formula of Circumsphere Radius of Dodecahedron given Face Diagonal is expressed as Circumsphere Radius of Dodecahedron = sqrt(3)/2*Face Diagonal of Dodecahedron. Here is an example- 13.85641 = sqrt(3)/2*16.

How to calculate Circumsphere Radius of Dodecahedron given Face Diagonal?

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

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

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

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

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

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

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

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

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