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Volume of Icosahedron given Total Surface Area 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{3 + \sqrt{5}}{12 \cdot \sqrt{5}} \cdot {(\frac{TSA}{\sqrt{3}})}^{\frac{3}{2}}

V - Volume of Icosahedron?TSA - Total Surface Area of Icosahedron?

Volume of Icosahedron given Total Surface Area Example

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Here is how the Volume of Icosahedron given Total Surface Area equation looks like with Values.

Here is how the Volume of Icosahedron given Total Surface Area equation looks like with Units.

Here is how the Volume of Icosahedron given Total Surface Area equation looks like.

2196.7314 = \frac{3 + \sqrt{5}}{12 \cdot \sqrt{5}} \cdot {(\frac{870}{\sqrt{3}})}^{\frac{3}{2}}

2196.7314m³ = \frac{3 + \sqrt{5}}{12 \cdot \sqrt{5}} \cdot {(\frac{870m²}{\sqrt{3}})}^{\frac{3}{2}}

2196.7314 = \frac{3 + \sqrt{5}}{12 \cdot \sqrt{5}} \cdot {(\frac{870}{\sqrt{3}})}^{\frac{3}{2}}

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Volume of Icosahedron given Total Surface Area Solution

Follow our step by step solution on how to calculate Volume of Icosahedron given Total Surface Area?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{3 + \sqrt{5}}{12 \cdot \sqrt{5}} \cdot {(\frac{870m²}{\sqrt{3}})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

V = \frac{3 + \sqrt{5}}{12 \cdot \sqrt{5}} \cdot {(\frac{870}{\sqrt{3}})}^{\frac{3}{2}}

Next Step Evaluate

∴

V = 2196.7314403308m³

LAST Step Rounding Answer

∴

V = 2196.7314m³

Volume of Icosahedron given Total Surface Area 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

Total Surface Area of Icosahedron

Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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 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 Total Surface Area?

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

How to evaluate Volume of Icosahedron given Total Surface Area using this online evaluator? To use this online evaluator for Volume of Icosahedron given Total Surface Area, enter Total Surface Area of Icosahedron (TSA) and hit the calculate button.

FAQs on Volume of Icosahedron given Total Surface Area

What is the formula to find Volume of Icosahedron given Total Surface Area?

The formula of Volume of Icosahedron given Total Surface Area is expressed as Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2). Here is an example- 2196.731 = (3+sqrt(5))/(12*sqrt(5))*(870/sqrt(3))^(3/2).

How to calculate Volume of Icosahedron given Total Surface Area?

With Total Surface Area of Icosahedron (TSA) we can find Volume of Icosahedron given Total Surface Area using the formula - Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2). 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))*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=5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Can the Volume of Icosahedron given Total Surface Area be negative?

No, the Volume of Icosahedron given Total Surface Area, measured in Volume cannot be negative.

Which unit is used to measure Volume of Icosahedron given Total Surface Area?

Volume of Icosahedron given Total Surface Area 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 Total Surface Area can be measured.

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