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Volume of Icosahedron given Face Area 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{4 \cdot A Face}{\sqrt{3}})}^{\frac{3}{2}}

V - Volume of Icosahedron?A_Face - Face Area of Icosahedron?

Volume of Icosahedron given Face Area Example

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Here is how the Volume of Icosahedron given Face Area equation looks like with Values.

Here is how the Volume of Icosahedron given Face Area equation looks like with Units.

Here is how the Volume of Icosahedron given Face Area equation looks like.

2311.3294 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 45}{\sqrt{3}})}^{\frac{3}{2}}

2311.3294m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 45m²}{\sqrt{3}})}^{\frac{3}{2}}

2311.3294 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 45}{\sqrt{3}})}^{\frac{3}{2}}

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Volume of Icosahedron given Face Area Solution

Follow our step by step solution on how to calculate Volume of Icosahedron given Face Area?

FIRST Step Consider the formula

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot A Face}{\sqrt{3}})}^{\frac{3}{2}}

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 45m²}{\sqrt{3}})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 45}{\sqrt{3}})}^{\frac{3}{2}}

Next Step Evaluate

∴

V = 2311.32944008659m³

LAST Step Rounding Answer

∴

V = 2311.3294m³

Volume of Icosahedron given Face Area 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

Face Area of Icosahedron

The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area 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 Face Area?

Volume of Icosahedron given Face Area evaluator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Face Area of Icosahedron)/sqrt(3))^(3/2) to evaluate the Volume of Icosahedron, The Volume of Icosahedron given Face Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the face area of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

How to evaluate Volume of Icosahedron given Face Area using this online evaluator? To use this online evaluator for Volume of Icosahedron given Face Area, enter Face Area of Icosahedron (A_Face) and hit the calculate button.

FAQs on Volume of Icosahedron given Face Area

What is the formula to find Volume of Icosahedron given Face Area?

The formula of Volume of Icosahedron given Face Area is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Face Area of Icosahedron)/sqrt(3))^(3/2). Here is an example- 2311.329 = 5/12*(3+sqrt(5))*((4*45)/sqrt(3))^(3/2).

How to calculate Volume of Icosahedron given Face Area?

With Face Area of Icosahedron (A_Face) we can find Volume of Icosahedron given Face Area using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Face Area of Icosahedron)/sqrt(3))^(3/2). 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 Face Area be negative?

No, the Volume of Icosahedron given Face Area, measured in Volume cannot be negative.

Which unit is used to measure Volume of Icosahedron given Face Area?

Volume of Icosahedron given Face Area 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 Face Area can be measured.

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