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Volume of Icosahedron given Face Perimeter 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{P Face}{3})}^{3}

V - Volume of Icosahedron?P_Face - Face Perimeter of Icosahedron?

Volume of Icosahedron given Face Perimeter Example

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

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

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

2181.695 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{30}{3})}^{3}

2181.695m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{30m}{3})}^{3}

2181.695 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{30}{3})}^{3}

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3D Geometry » fx Volume of Icosahedron given Face Perimeter

Volume of Icosahedron given Face Perimeter Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{30m}{3})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{30}{3})}^{3}

Next Step Evaluate

∴

V = 2181.69499062491m³

LAST Step Rounding Answer

∴

V = 2181.695m³

Volume of Icosahedron given Face Perimeter 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 Perimeter of Icosahedron

Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.

Symbol: P_Face

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Face Perimeter 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 Perimeter?

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

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

FAQs on Volume of Icosahedron given Face Perimeter

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

The formula of Volume of Icosahedron given Face Perimeter is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^3. Here is an example- 2181.695 = 5/12*(3+sqrt(5))*(30/3)^3.

How to calculate Volume of Icosahedron given Face Perimeter?

With Face Perimeter of Icosahedron (P_Face) we can find Volume of Icosahedron given Face Perimeter using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^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 Face Perimeter be negative?

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

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

Volume of Icosahedron given Face Perimeter 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 Perimeter can be measured.

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