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Volume of Icosahedron given Lateral Surface Area 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 LSA}{9 \cdot \sqrt{3}})}^{\frac{3}{2}}

V - Volume of Icosahedron?LSA - Lateral Surface Area of Icosahedron?

Volume of Icosahedron given Lateral Surface Area Example

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

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

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

2184.1186 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 780}{9 \cdot \sqrt{3}})}^{\frac{3}{2}}

2184.1186m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}})}^{\frac{3}{2}}

2184.1186 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 780}{9 \cdot \sqrt{3}})}^{\frac{3}{2}}

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Volume of Icosahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot LSA}{9 \cdot \sqrt{3}})}^{\frac{3}{2}}

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{2 \cdot 780}{9 \cdot \sqrt{3}})}^{\frac{3}{2}}

Next Step Evaluate

∴

V = 2184.11864753849m³

LAST Step Rounding Answer

∴

V = 2184.1186m³

Volume of Icosahedron given Lateral 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

Lateral Surface Area of Icosahedron

Lateral Surface Area of Icosahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral 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 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 Lateral Surface Area?

Volume of Icosahedron given Lateral Surface Area evaluator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))^(3/2) to evaluate the Volume of Icosahedron, The Volume of Icosahedron given Lateral Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the lateral surface area of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

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

FAQs on Volume of Icosahedron given Lateral Surface Area

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

The formula of Volume of Icosahedron given Lateral Surface Area is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))^(3/2). Here is an example- 2184.119 = 5/12*(3+sqrt(5))*((2*780)/(9*sqrt(3)))^(3/2).

How to calculate Volume of Icosahedron given Lateral Surface Area?

With Lateral Surface Area of Icosahedron (LSA) we can find Volume of Icosahedron given Lateral Surface Area using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))^(3/2). 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=(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 Lateral Surface Area be negative?

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

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

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

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