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Circumsphere Radius of Dodecahedron given Volume Formula

GoCircumsphere Radius of Dodecahedron Formula

GoCircumsphere Radius of Dodecahedron given Face Diagonal 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 {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

r_c - Circumsphere Radius of Dodecahedron?V - Volume of Dodecahedron?

Circumsphere Radius of Dodecahedron given Volume Example

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

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

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

14.035 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

14.035m = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

14.035 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

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Circumsphere Radius of Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Evaluate

∴

r c = 14.0350293285297m

LAST Step Rounding Answer

∴

r c = 14.035m

Circumsphere Radius of Dodecahedron given Volume 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

Volume of Dodecahedron

Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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 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})}}}

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 Volume?

Circumsphere Radius of Dodecahedron given Volume evaluator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3) to evaluate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Volume 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 volume of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Dodecahedron given Volume

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

The formula of Circumsphere Radius of Dodecahedron given Volume is expressed as Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). Here is an example- 14.03503 = sqrt(3)*(1+sqrt(5))/4*((4*7700)/(15+(7*sqrt(5))))^(1/3).

How to calculate Circumsphere Radius of Dodecahedron given Volume?

With Volume of Dodecahedron (V) we can find Circumsphere Radius of Dodecahedron given Volume using the formula - Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). This formula also uses Square Root Function 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)/2*Face Diagonal of Dodecahedron
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 Volume be negative?

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

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

Circumsphere Radius of Dodecahedron given Volume 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 Volume can be measured.

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