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Volume of Great Dodecahedron given Surface to Volume Ratio 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{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot R A/V})}^{3}

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

Volume of Great Dodecahedron given Surface to Volume Ratio Example

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

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

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

1580.7313 = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7})}^{3}

1580.7313m³ = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7m⁻¹})}^{3}

1580.7313 = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7})}^{3}

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Volume of Great Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7m⁻¹})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{4} \cdot (\sqrt{5} - 1) \cdot {(\frac{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}{\frac{5}{4} \cdot (\sqrt{5} - 1) \cdot 0.7})}^{3}

Next Step Evaluate

∴

V = 1580.73126207817m³

LAST Step Rounding Answer

∴

V = 1580.7313m³

Volume of Great Dodecahedron given Surface to Volume Ratio 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

Surface to Volume Ratio of Great Dodecahedron

Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great 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 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 Circumsphere Radius

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

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

Volume of Great Dodecahedron given Surface to Volume Ratio evaluator uses Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron))^3 to evaluate the Volume of Great Dodecahedron, Volume of Great Dodecahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron, calculated using its surface to volume ratio. Volume of Great Dodecahedron is denoted by V symbol.

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

FAQs on Volume of Great Dodecahedron given Surface to Volume Ratio

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

The formula of Volume of Great Dodecahedron given Surface to Volume Ratio is expressed as Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron))^3. Here is an example- 1580.731 = 5/4*(sqrt(5)-1)*((15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7))^3.

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

With Surface to Volume Ratio of Great Dodecahedron (R_A/V) we can find Volume of Great Dodecahedron given Surface to Volume Ratio using the formula - Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron))^3. This formula also uses Square Root (sqrt) 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)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3

Can the Volume of Great Dodecahedron given Surface to Volume Ratio be negative?

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

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

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

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