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Circumsphere Radius of Great Stellated Dodecahedron given Volume Formula

GoCircumsphere Radius of Great Stellated Dodecahedron Formula

GoCircumsphere Radius of Great Stellated Dodecahedron given Ridge Length Formula

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

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

r_c - Circumradius of Great Stellated Dodecahedron?V - Volume of Great Stellated Dodecahedron?

Circumsphere Radius of Great Stellated Dodecahedron given Volume Example

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

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

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

22.6785 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot {(\frac{4 \cdot 6550}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

22.6785m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot {(\frac{4 \cdot 6550m³}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

22.6785 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot {(\frac{4 \cdot 6550}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

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Circumsphere Radius of Great Stellated Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot {(\frac{4 \cdot 6550m³}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot {(\frac{4 \cdot 6550}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

Next Step Evaluate

∴

r c = 22.6785133878573m

LAST Step Rounding Answer

∴

r c = 22.6785m

Circumsphere Radius of Great Stellated Dodecahedron given Volume Formula Elements

Variables

Functions

Circumradius of Great Stellated Dodecahedron

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

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Great Stellated Dodecahedron

Volume of Great Stellated Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Great Stellated 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 Circumradius of Great Stellated Dodecahedron

Go Circumsphere Radius of Great Stellated Dodecahedron

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

Go Circumsphere Radius of Great Stellated Dodecahedron given Ridge Length

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{2} \cdot \frac{1 \cdot l Ridge}{1 + \sqrt{5}}

Go Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \frac{l c(Pentagram)}{2 + \sqrt{5}}

Go Circumsphere Radius of Great Stellated Dodecahedron given Pyramidal Height

r c = \frac{3 \cdot h Pyramid}{2}

How to Evaluate Circumsphere Radius of Great Stellated Dodecahedron given Volume?

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

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

FAQs on Circumsphere Radius of Great Stellated Dodecahedron given Volume

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

The formula of Circumsphere Radius of Great Stellated Dodecahedron given Volume is expressed as Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3). Here is an example- 22.67851 = (sqrt(3)*(3+sqrt(5)))/4*((4*6550)/(5*(3+sqrt(5))))^(1/3).

How to calculate Circumsphere Radius of Great Stellated Dodecahedron given Volume?

With Volume of Great Stellated Dodecahedron (V) we can find Circumsphere Radius of Great Stellated Dodecahedron given Volume using the formula - Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(1/3). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Great Stellated Dodecahedron?

Here are the different ways to Calculate Circumradius of Great Stellated Dodecahedron-

Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/4*Edge Length of Great Stellated Dodecahedron
Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/2*(1*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))

Can the Circumsphere Radius of Great Stellated Dodecahedron given Volume be negative?

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

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

Circumsphere Radius of Great Stellated 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 Great Stellated Dodecahedron given Volume can be measured.

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