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Volume of Truncated Dodecahedron given Surface to Volume Ratio 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{12 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{R A/V \cdot (99 + (47 \cdot \sqrt{5}))})}^{3}

V - Volume of Truncated Dodecahedron?R_A/V - Surface to Volume Ratio of Truncated Dodecahedron?

Volume of Truncated Dodecahedron given Surface to Volume Ratio Example

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Here is how the Volume of Truncated Dodecahedron given Surface to Volume Ratio equation looks like with Values.

Here is how the Volume of Truncated Dodecahedron given Surface to Volume Ratio equation looks like with Units.

Here is how the Volume of Truncated Dodecahedron given Surface to Volume Ratio equation looks like.

142430.1221 = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{12 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1 \cdot (99 + (47 \cdot \sqrt{5}))})}^{3}

142430.1221m³ = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{12 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1m⁻¹ \cdot (99 + (47 \cdot \sqrt{5}))})}^{3}

142430.1221 = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{12 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1 \cdot (99 + (47 \cdot \sqrt{5}))})}^{3}

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Volume of Truncated Dodecahedron given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Volume of Truncated Dodecahedron given Surface to Volume Ratio?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{12 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1m⁻¹ \cdot (99 + (47 \cdot \sqrt{5}))})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (99 + (47 \cdot \sqrt{5})) \cdot {(\frac{12 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1 \cdot (99 + (47 \cdot \sqrt{5}))})}^{3}

Next Step Evaluate

∴

V = 142430.122074108m³

LAST Step Rounding Answer

∴

V = 142430.1221m³

Volume of Truncated Dodecahedron given Surface to Volume Ratio 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

Surface to Volume Ratio of Truncated Dodecahedron

Surface to Volume Ratio of Truncated Dodecahedron is the numerical ratio of the total surface area of a Truncated Dodecahedron to the volume of the Truncated Dodecahedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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 Circumsphere Radius

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

How to Evaluate Volume of Truncated Dodecahedron given Surface to Volume Ratio?

Volume of Truncated Dodecahedron given Surface to Volume Ratio evaluator uses Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))))^3 to evaluate the Volume of Truncated Dodecahedron, Volume of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron, and calculated using the surface to volume ratio of the Truncated Dodecahedron. Volume of Truncated Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Truncated Dodecahedron given Surface to Volume Ratio

What is the formula to find Volume of Truncated Dodecahedron given Surface to Volume Ratio?

The formula of Volume of Truncated Dodecahedron given Surface to Volume Ratio is expressed as Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))))^3. Here is an example- 142430.1 = 5/12*(99+(47*sqrt(5)))*((12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5)))))^3.

How to calculate Volume of Truncated Dodecahedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Truncated Dodecahedron (R_A/V) we can find Volume of Truncated Dodecahedron given Surface to Volume Ratio using the formula - Volume of Truncated Dodecahedron = 5/12*(99+(47*sqrt(5)))*((12*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*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 Surface to Volume Ratio be negative?

No, the Volume of Truncated Dodecahedron given Surface to Volume Ratio, measured in Volume cannot be negative.

Which unit is used to measure Volume of Truncated Dodecahedron given Surface to Volume Ratio?

Volume of Truncated Dodecahedron given Surface to Volume Ratio 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 Surface to Volume Ratio can be measured.

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