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Circumsphere Radius of Great Dodecahedron given Ridge Length Formula

GoCircumsphere Radius of Great Dodecahedron Formula

GoCircumsphere Radius of Great Dodecahedron given Pyramidal Height Formula

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

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot l Ridge}{\sqrt{5} - 1}

r_c - Circumsphere Radius of Great Dodecahedron?l_Ridge - Ridge Length of Great Dodecahedron?

Circumsphere Radius of Great Dodecahedron given Ridge Length Example

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Here is how the Circumsphere Radius of Great Dodecahedron given Ridge Length equation looks like with Values.

Here is how the Circumsphere Radius of Great Dodecahedron given Ridge Length equation looks like with Units.

Here is how the Circumsphere Radius of Great Dodecahedron given Ridge Length equation looks like.

9.2331 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot 6}{\sqrt{5} - 1}

9.2331m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot 6m}{\sqrt{5} - 1}

9.2331 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot 6}{\sqrt{5} - 1}

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Circumsphere Radius of Great Dodecahedron given Ridge Length Solution

Follow our step by step solution on how to calculate Circumsphere Radius of Great Dodecahedron given Ridge Length?

FIRST Step Consider the formula

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot l Ridge}{\sqrt{5} - 1}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot 6m}{\sqrt{5} - 1}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot 6}{\sqrt{5} - 1}

Next Step Evaluate

∴

r c = 9.23305061152576m

LAST Step Rounding Answer

∴

r c = 9.2331m

Circumsphere Radius of Great Dodecahedron given Ridge Length Formula Elements

Variables

Functions

Circumsphere Radius of Great Dodecahedron

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

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Great Dodecahedron

Ridge Length of Great Dodecahedron

Ridge Length of Great Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Dodecahedron.

Symbol: l_Ridge

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Ridge Length of Great 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 Great Dodecahedron

Go Circumsphere Radius of Great Dodecahedron

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot l e

Go Circumsphere Radius of Great Dodecahedron given Pyramidal Height

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 - \sqrt{5})}

Go Circumsphere Radius of Great Dodecahedron given Total Surface Area

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

Go Circumsphere Radius of Great Dodecahedron given Volume

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot V}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

How to Evaluate Circumsphere Radius of Great Dodecahedron given Ridge Length?

Circumsphere Radius of Great Dodecahedron given Ridge Length evaluator uses Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1) to evaluate the Circumsphere Radius of Great Dodecahedron, Circumsphere Radius of Great Dodecahedron given Ridge Length formula is defined as the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere, calculated using its ridge length. Circumsphere Radius of Great Dodecahedron is denoted by r_c symbol.

How to evaluate Circumsphere Radius of Great Dodecahedron given Ridge Length using this online evaluator? To use this online evaluator for Circumsphere Radius of Great Dodecahedron given Ridge Length, enter Ridge Length of Great Dodecahedron (l_Ridge) and hit the calculate button.

FAQs on Circumsphere Radius of Great Dodecahedron given Ridge Length

What is the formula to find Circumsphere Radius of Great Dodecahedron given Ridge Length?

The formula of Circumsphere Radius of Great Dodecahedron given Ridge Length is expressed as Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1). Here is an example- 9.233051 = sqrt(10+(2*sqrt(5)))/4*(2*6)/(sqrt(5)-1).

How to calculate Circumsphere Radius of Great Dodecahedron given Ridge Length?

With Ridge Length of Great Dodecahedron (l_Ridge) we can find Circumsphere Radius of Great Dodecahedron given Ridge Length using the formula - Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1). This formula also uses Square Root Function function(s).

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

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

Circumsphere Radius of Great Dodecahedron=sqrt(10+(2*sqrt(5)))/4*Edge Length of Great Dodecahedron
Circumsphere Radius of Great Dodecahedron=sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))
Circumsphere Radius of Great Dodecahedron=sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

Can the Circumsphere Radius of Great Dodecahedron given Ridge Length be negative?

No, the Circumsphere Radius of Great Dodecahedron given Ridge Length, measured in Length cannot be negative.

Which unit is used to measure Circumsphere Radius of Great Dodecahedron given Ridge Length?

Circumsphere Radius of Great Dodecahedron given Ridge Length 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 Great Dodecahedron given Ridge Length can be measured.

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