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Circumsphere Radius of Dodecahedron given Face Area 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 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

r_c - Circumsphere Radius of Dodecahedron?A_Face - Face Area of Dodecahedron?

Circumsphere Radius of Dodecahedron given Face Area Example

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

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

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

14.1323 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

14.1323m = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

14.1323 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

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Circumsphere Radius of Dodecahedron given Face Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

r c = 14.1322987663714m

LAST Step Rounding Answer

∴

r c = 14.1323m

Circumsphere Radius of Dodecahedron given Face Area 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 Area of Dodecahedron

The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area 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 Face Diagonal

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

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})}}}

How to Evaluate Circumsphere Radius of Dodecahedron given Face Area?

Circumsphere Radius of Dodecahedron given Face Area evaluator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5)))) to evaluate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Face Area 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 area of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Dodecahedron given Face Area

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

The formula of Circumsphere Radius of Dodecahedron given Face Area is expressed as Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5)))). Here is an example- 14.1323 = sqrt(3)*(1+sqrt(5))/4*sqrt((4*175)/sqrt(25+(10*sqrt(5)))).

How to calculate Circumsphere Radius of Dodecahedron given Face Area?

With Face Area of Dodecahedron (A_Face) we can find Circumsphere Radius of Dodecahedron given Face Area using the formula - Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5)))). 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)/2*Face Diagonal of Dodecahedron

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

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

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

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

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