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Volume of Icosahedron Formula

GoVolume of Icosahedron given Circumsphere Radius Formula

GoVolume of Icosahedron given Insphere Radius 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 {l e}^{3}

V - Volume of Icosahedron?l_e - Edge Length of Icosahedron?

Volume of Icosahedron Example

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

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

Here is how the Volume of Icosahedron equation looks like.

2181.695 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot 10^{3}

2181.695m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {10m}^{3}

2181.695 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot 10^{3}

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Volume of Icosahedron Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {10m}^{3}

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

V = 2181.69499062491m³

LAST Step Rounding Answer

∴

V = 2181.695m³

Volume of Icosahedron 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

Edge Length of Icosahedron

Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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 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}

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}}

How to Evaluate Volume of Icosahedron?

Volume of Icosahedron evaluator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3 to evaluate the Volume of Icosahedron, Volume of Icosahedron formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

How to evaluate Volume of Icosahedron using this online evaluator? To use this online evaluator for Volume of Icosahedron, enter Edge Length of Icosahedron (l_e) and hit the calculate button.

FAQs on Volume of Icosahedron

What is the formula to find Volume of Icosahedron?

The formula of Volume of Icosahedron is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3. Here is an example- 2181.695 = 5/12*(3+sqrt(5))*10^3.

How to calculate Volume of Icosahedron?

With Edge Length of Icosahedron (l_e) we can find Volume of Icosahedron using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length 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=5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3
Volume of Icosahedron=5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3
Volume of Icosahedron=(3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Can the Volume of Icosahedron be negative?

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

Which unit is used to measure Volume of Icosahedron?

Volume of Icosahedron 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 can be measured.

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