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Volume of Icosahedron given Midsphere Radius 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 r m}{1 + \sqrt{5}})}^{3}

V - Volume of Icosahedron?r_m - Midsphere Radius of Icosahedron?

Volume of Icosahedron given Midsphere Radius Example

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

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

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

2109.556 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 8}{1 + \sqrt{5}})}^{3}

2109.556m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 8m}{1 + \sqrt{5}})}^{3}

2109.556 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 8}{1 + \sqrt{5}})}^{3}

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Volume of Icosahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot r m}{1 + \sqrt{5}})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 8m}{1 + \sqrt{5}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 8}{1 + \sqrt{5}})}^{3}

Next Step Evaluate

∴

V = 2109.55601493297m³

LAST Step Rounding Answer

∴

V = 2109.556m³

Volume of Icosahedron given Midsphere 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

Midsphere Radius of Icosahedron

The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere 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 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 Midsphere Radius?

Volume of Icosahedron given Midsphere Radius evaluator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^3 to evaluate the Volume of Icosahedron, The Volume of Icosahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the midsphere radius of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

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

FAQs on Volume of Icosahedron given Midsphere Radius

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

The formula of Volume of Icosahedron given Midsphere Radius is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^3. Here is an example- 2109.556 = 5/12*(3+sqrt(5))*((4*8)/(1+sqrt(5)))^3.

How to calculate Volume of Icosahedron given Midsphere Radius?

With Midsphere Radius of Icosahedron (r_m) we can find Volume of Icosahedron given Midsphere Radius using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+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 Midsphere Radius be negative?

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

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

Volume of Icosahedron given Midsphere 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 Midsphere Radius can be measured.

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