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Volume of Great Dodecahedron given Circumsphere Radius Formula

GoVolume of Great Dodecahedron Formula

GoVolume of Great Dodecahedron given Ridge Length Formula

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

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

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

Volume of Great Dodecahedron given Circumsphere Radius Example

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

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

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

1309.3656 = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

1309.3656m³ = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

1309.3656 = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

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Volume of Great Dodecahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Evaluate

∴

V = 1309.36557970607m³

LAST Step Rounding Answer

∴

V = 1309.3656m³

Volume of Great Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Volume of Great Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Great Dodecahedron

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

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 Dodecahedron

Go Volume of Great Dodecahedron

V = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {l e}^{3}

Go Volume of Great Dodecahedron given Ridge Length

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

Go Volume of Great Dodecahedron given Pyramidal Height

V = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 - \sqrt{5})})}^{3}

Go Volume of Great Dodecahedron given Total Surface Area

V = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}})}^{\frac{3}{2}}

How to Evaluate Volume of Great Dodecahedron given Circumsphere Radius?

Volume of Great Dodecahedron given Circumsphere Radius evaluator uses Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3 to evaluate the Volume of Great Dodecahedron, Volume of Great Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron, calculated using its circumsphere radius. Volume of Great Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Great Dodecahedron given Circumsphere Radius

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

The formula of Volume of Great Dodecahedron given Circumsphere Radius is expressed as Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3. Here is an example- 1309.366 = 5/4*(sqrt(5)-1)*((4*9)/sqrt(10+(2*sqrt(5))))^3.

How to calculate Volume of Great Dodecahedron given Circumsphere Radius?

With Circumsphere Radius of Great Dodecahedron (r_c) we can find Volume of Great Dodecahedron given Circumsphere Radius using the formula - Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3. This formula also uses Square Root Function function(s).

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

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

Volume of Great Dodecahedron=5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3
Volume of Great Dodecahedron=5/4*(sqrt(5)-1)*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^3
Volume of Great Dodecahedron=5/4*(sqrt(5)-1)*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^3

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

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

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

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

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