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Circumsphere Radius of Truncated Dodecahedron given Volume Formula

GoCircumsphere Radius of Truncated Dodecahedron Formula

GoCircumsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

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

Circumsphere Radius of Truncated Dodecahedron given Volume Example

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

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

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

29.6899 = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot 85000}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

29.6899m = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot 85000m³}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

29.6899 = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot 85000}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

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Circumsphere Radius of Truncated Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot 85000m³}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot 85000}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Next Step Evaluate

∴

r c = 29.6898726975055m

LAST Step Rounding Answer

∴

r c = 29.6899m

Circumsphere Radius of Truncated Dodecahedron given Volume Formula Elements

Variables

Functions

Circumsphere Radius of Truncated Dodecahedron

Circumsphere Radius of Truncated Dodecahedron is the radius of the sphere that contains the Truncated 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 Truncated Dodecahedron

Volume of Truncated Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Truncated 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 Truncated Dodecahedron

Go Circumsphere Radius of Truncated Dodecahedron

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot l e

Go Circumsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \frac{l e(Dodecahedron)}{\sqrt{5}}

Go Circumsphere Radius of Truncated Dodecahedron given Total Surface Area

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{TSA}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

Go Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius

r c = \sqrt{74 + (30 \cdot \sqrt{5})} \cdot \frac{r m}{5 + (3 \cdot \sqrt{5})}

How to Evaluate Circumsphere Radius of Truncated Dodecahedron given Volume?

Circumsphere Radius of Truncated Dodecahedron given Volume evaluator uses Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3) to evaluate the Circumsphere Radius of Truncated Dodecahedron, Circumsphere Radius of Truncated Dodecahedron given Volume formula is defined as the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the volume of the Truncated Dodecahedron. Circumsphere Radius of Truncated Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Truncated Dodecahedron given Volume

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

The formula of Circumsphere Radius of Truncated Dodecahedron given Volume is expressed as Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3). Here is an example- 29.68987 = sqrt(74+(30*sqrt(5)))/4*((12*85000)/(5*(99+(47*sqrt(5)))))^(1/3).

How to calculate Circumsphere Radius of Truncated Dodecahedron given Volume?

With Volume of Truncated Dodecahedron (V) we can find Circumsphere Radius of Truncated Dodecahedron given Volume using the formula - Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3). This formula also uses Square Root (sqrt) function(s).

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

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

Circumsphere Radius of Truncated Dodecahedron=sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
Circumsphere Radius of Truncated Dodecahedron=sqrt(74+(30*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Circumsphere Radius of Truncated Dodecahedron=sqrt(74+(30*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*(sqrt(5+(2*sqrt(5))))))))

Can the Circumsphere Radius of Truncated Dodecahedron given Volume be negative?

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

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

Circumsphere Radius of Truncated 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 Truncated Dodecahedron given Volume can be measured.

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