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Volume of Icosahedron given Insphere Radius Formula

GoVolume of Icosahedron Formula

GoVolume of Icosahedron given Circumsphere 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 {(\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

V - Volume of Icosahedron?r_i - Insphere Radius of Icosahedron?

Volume of Icosahedron given Insphere Radius Example

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

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

Here is how the Volume of Icosahedron given Insphere Radius equation looks like.

1733.5413 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

1733.5413m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

1733.5413 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

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Volume of Icosahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{3}

Next Step Evaluate

∴

V = 1733.54125725442m³

LAST Step Rounding Answer

∴

V = 1733.5413m³

Volume of Icosahedron given Insphere Radius 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

Insphere Radius of Icosahedron

Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius 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

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 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 given Insphere Radius?

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

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

FAQs on Volume of Icosahedron given Insphere Radius

What is the formula to find Volume of Icosahedron given Insphere Radius?

The formula of Volume of Icosahedron given Insphere Radius is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3. Here is an example- 1733.541 = 5/12*(3+sqrt(5))*((12*7)/(sqrt(3)*(3+sqrt(5))))^3.

How to calculate Volume of Icosahedron given Insphere Radius?

With Insphere Radius of Icosahedron (r_i) we can find Volume of Icosahedron given Insphere Radius using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3. This formula also uses Square Root Function 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))*Edge Length of Icosahedron^3
Volume of Icosahedron=5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*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 given Insphere Radius be negative?

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

Which unit is used to measure Volume of Icosahedron given Insphere Radius?

Volume of Icosahedron given Insphere Radius 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 Insphere Radius can be measured.

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