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Volume of Great Stellated Dodecahedron given Circumradius Formula

GoVolume of Great Stellated Dodecahedron Formula

GoVolume of Great Stellated Dodecahedron given Ridge Length Formula

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

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

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

Volume of Great Stellated Dodecahedron given Circumradius Example

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

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

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

6832.5223 = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 23}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

6832.5223m³ = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 23m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

6832.5223 = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 23}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

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Volume of Great Stellated Dodecahedron given Circumradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 23m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 23}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

Next Step Evaluate

∴

V = 6832.52234435199m³

LAST Step Rounding Answer

∴

V = 6832.5223m³

Volume of Great Stellated Dodecahedron given Circumradius Formula Elements

Variables

Functions

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

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

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 Volume of Great Stellated Dodecahedron

Go Volume of Great Stellated Dodecahedron

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {l e}^{3}

Go Volume of Great Stellated Dodecahedron given Ridge Length

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot l Ridge}{1 + \sqrt{5}})}^{3}

Go Volume of Great Stellated Dodecahedron given Pentagram Chord

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

Go Volume of Great Stellated Dodecahedron given Pyramidal Height

V = \frac{5}{4} \cdot (3 + \sqrt{5}) \cdot {(\frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

How to Evaluate Volume of Great Stellated Dodecahedron given Circumradius?

Volume of Great Stellated Dodecahedron given Circumradius evaluator uses Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3 to evaluate the Volume of Great Stellated Dodecahedron, Volume of Great Stellated Dodecahedron given Circumradius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron, calculated using its circumradius. Volume of Great Stellated Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Great Stellated Dodecahedron given Circumradius

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

The formula of Volume of Great Stellated Dodecahedron given Circumradius is expressed as Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3. Here is an example- 6832.522 = 5/4*(3+sqrt(5))*((4*23)/(sqrt(3)*(3+sqrt(5))))^3.

How to calculate Volume of Great Stellated Dodecahedron given Circumradius?

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

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

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

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

Can the Volume of Great Stellated Dodecahedron given Circumradius be negative?

No, the Volume of Great Stellated Dodecahedron given Circumradius, measured in Volume cannot be negative.

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

Volume of Great Stellated Dodecahedron given Circumradius is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Great Stellated Dodecahedron given Circumradius can be measured.

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