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Volume of Icosahedron given Space Diagonal 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{2 \cdot d Space}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

V - Volume of Icosahedron?d_Space - Space Diagonal of Icosahedron?

Volume of Icosahedron given Space Diagonal Example

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

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

Here is how the Volume of Icosahedron given Space Diagonal equation looks like.

2174.4322 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

2174.4322m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

2174.4322 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

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Volume of Icosahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot d Space}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Evaluate

∴

V = 2174.43221508949m³

LAST Step Rounding Answer

∴

V = 2174.4322m³

Volume of Icosahedron given Space Diagonal 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

Space Diagonal of Icosahedron

The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal 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 Space Diagonal?

Volume of Icosahedron given Space Diagonal evaluator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3 to evaluate the Volume of Icosahedron, The Volume of Icosahedron given Space Diagonal formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the space diagonal of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

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

FAQs on Volume of Icosahedron given Space Diagonal

What is the formula to find Volume of Icosahedron given Space Diagonal?

The formula of Volume of Icosahedron given Space Diagonal is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3. Here is an example- 2174.432 = 5/12*(3+sqrt(5))*((2*19)/(sqrt(10+(2*sqrt(5)))))^3.

How to calculate Volume of Icosahedron given Space Diagonal?

With Space Diagonal of Icosahedron (d_Space) we can find Volume of Icosahedron given Space Diagonal using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^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 Space Diagonal be negative?

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

Which unit is used to measure Volume of Icosahedron given Space Diagonal?

Volume of Icosahedron given Space Diagonal 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 Space Diagonal can be measured.

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