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Volume of Truncated Dodecahedron given Circumsphere Radius Formula

GoVolume of Truncated Dodecahedron Formula

GoVolume of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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

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

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

Volume of Truncated Dodecahedron given Circumsphere Radius Example

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

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

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

87691.5373 = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 30}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{3}

87691.5373m³ = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 30m}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{3}

87691.5373 = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 30}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{3}

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Volume of Truncated Dodecahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

V = 87691.5372678378m³

LAST Step Rounding Answer

∴

V = 87691.5373m³

Volume of Truncated Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

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

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

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 Truncated Dodecahedron

Go Volume of Truncated Dodecahedron

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {l e}^{3}

Go Volume of Truncated Dodecahedron given Dodecahedral Edge Length

V = \frac{99 + (47 \cdot \sqrt{5})}{12 \cdot \sqrt{5}} \cdot {l e(Dodecahedron)}^{3}

Go Volume of Truncated Dodecahedron given Total Surface Area

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\sqrt{\frac{TSA}{5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}})}^{3}

Go Volume of Truncated Dodecahedron given Midsphere Radius

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot r m}{5 + (3 \cdot \sqrt{5})})}^{3}

How to Evaluate Volume of Truncated Dodecahedron given Circumsphere Radius?

Volume of Truncated Dodecahedron given Circumsphere Radius evaluator uses Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^3 to evaluate the Volume of Truncated Dodecahedron, Volume of Truncated Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron. Volume of Truncated Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Truncated Dodecahedron given Circumsphere Radius

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

The formula of Volume of Truncated Dodecahedron given Circumsphere Radius is expressed as Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^3. Here is an example- 87691.54 = 5/12*(99+(47*sqrt(5)))*((4*30)/(sqrt(74+(30*sqrt(5)))))^3.

How to calculate Volume of Truncated Dodecahedron given Circumsphere Radius?

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

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

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

Volume of Truncated Dodecahedron=5/12*(99+(47*sqrt(5)))*Edge Length of Truncated Dodecahedron^3
Volume of Truncated Dodecahedron=(99+(47*sqrt(5)))/(12*sqrt(5))*Dodecahedral Edge Length of Truncated Dodecahedron^3
Volume of Truncated Dodecahedron=5/12*(99+(47*sqrt(5)))*(sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))))^3

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

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

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

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

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