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Volume of Icosahedron given Surface to Volume Ratio Formula

GoVolume of Icosahedron given Total Surface Area Formula

GoVolume of Icosahedron Formula

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

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

V - Volume of Icosahedron?R_A/V - Surface to Volume Ratio of Icosahedron?

Volume of Icosahedron given Surface to Volume Ratio Example

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

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

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

2132.1799 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4})}^{3}

2132.1799m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4m⁻¹})}^{3}

2132.1799 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4})}^{3}

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Volume of Icosahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4m⁻¹})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4})}^{3}

Next Step Evaluate

∴

V = 2132.17993558079m³

LAST Step Rounding Answer

∴

V = 2132.1799m³

Volume of Icosahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Volume of Icosahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Icosahedron

Surface to Volume Ratio of Icosahedron

The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Icosahedron

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 Icosahedron

Go Volume of Icosahedron given Total Surface Area

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

Go Volume of Icosahedron

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

Go Volume of Icosahedron given Circumsphere Radius

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Go Volume of Icosahedron given Insphere Radius

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

How to Evaluate Volume of Icosahedron given Surface to Volume Ratio?

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

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

FAQs on Volume of Icosahedron given Surface to Volume Ratio

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

The formula of Volume of Icosahedron given Surface to Volume Ratio is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3. Here is an example- 2132.18 = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*0.4))^3.

How to calculate Volume of Icosahedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Icosahedron (R_A/V) we can find Volume of Icosahedron given Surface to Volume Ratio using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Icosahedron?

Here are the different ways to Calculate Volume of Icosahedron-

Volume of Icosahedron=(3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)
Volume of Icosahedron=5/12*(3+sqrt(5))*Edge Length of Icosahedron^3
Volume of Icosahedron=5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Can the Volume of Icosahedron given Surface to Volume Ratio be negative?

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

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

Volume of Icosahedron 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 Icosahedron given Surface to Volume Ratio can be measured.

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