FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Volume of Icosahedron given Circumsphere Radius Formula

GoVolume of Icosahedron Formula

GoVolume of Icosahedron given Insphere Radius Formula

Fx Copy

LaTeX Copy

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 c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

V - Volume of Icosahedron?r_c - Circumsphere Radius of Icosahedron?

Volume of Icosahedron given Circumsphere Radius Example

With values

With units

Only example

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

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

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

1848.8539 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

1848.8539m³ = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

1848.8539 = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Volume of Icosahedron given Circumsphere Radius

Volume of Icosahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{12} \cdot (3 + \sqrt{5}) \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{3}

Next Step Evaluate

∴

V = 1848.85386767778m³

LAST Step Rounding Answer

∴

V = 1848.8539m³

Volume of Icosahedron given Circumsphere 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

Circumsphere Radius of Icosahedron

Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere 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

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

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}}

How to Evaluate Volume of Icosahedron given Circumsphere Radius?

Volume of Icosahedron given Circumsphere Radius evaluator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3 to evaluate the Volume of Icosahedron, Volume of Icosahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the circumsphere radius of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

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

FAQs on Volume of Icosahedron given Circumsphere Radius

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

The formula of Volume of Icosahedron given Circumsphere Radius is expressed as Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3. Here is an example- 1848.854 = 5/12*(3+sqrt(5))*((4*9)/(sqrt(10+(2*sqrt(5)))))^3.

How to calculate Volume of Icosahedron given Circumsphere Radius?

With Circumsphere Radius of Icosahedron (r_c) we can find Volume of Icosahedron given Circumsphere Radius using the formula - Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius 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=5/12*(3+sqrt(5))*Edge Length of Icosahedron^3
Volume of Icosahedron=5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3
Volume of Icosahedron=(3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Can the Volume of Icosahedron given Circumsphere Radius be negative?

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

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

Volume of Icosahedron given Circumsphere 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 Circumsphere Radius can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit