Volume of Hexakis Icosahedron given Midsphere Radius Calculator

✖Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Hexakis Icosahedron [r_m]

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✖Volume of Hexakis Icosahedron is the quantity of three dimensional space enclosed by the entire surface of Hexakis Icosahedron .ⓘ Volume of Hexakis Icosahedron given Midsphere Radius [V]

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Formula

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Volume of Hexakis Icosahedron given Midsphere Radius

Formula

`"V" = 25/88*((8*"r"_{"m"})/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))`

Example

`"14379.4m³"=25/88*((8*"15m")/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))`

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Volume of Hexakis Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Hexakis Icosahedron = 25/88*((8*Midsphere Radius of Hexakis Icosahedron)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))
V = 25/88*((8*r_m)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Volume of Hexakis Icosahedron - (Measured in Cubic Meter) - Volume of Hexakis Icosahedron is the quantity of three dimensional space enclosed by the entire surface of Hexakis Icosahedron .
Midsphere Radius of Hexakis Icosahedron - (Measured in Meter) - Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Hexakis Icosahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 25/88*((8*r_m)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5))) --> 25/88*((8*15)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))

Evaluating ... ...

V = 14379.396757825

STEP 3: Convert Result to Output's Unit

14379.396757825 Cubic Meter --> No Conversion Required

FINAL ANSWER

14379.396757825 ≈ 14379.4 Cubic Meter <-- Volume of Hexakis Icosahedron

(Calculation completed in 00.004 seconds)

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< 8 Volume of Hexakis Icosahedron Calculators

Volume of Hexakis Icosahedron given Surface to Volume Ratio

Go Volume of Hexakis Icosahedron = 25/88*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))^3*sqrt(6*(185+82*sqrt(5)))

Volume of Hexakis Icosahedron given Total Surface Area

Go Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((44*Total Surface Area of Hexakis Icosahedron)/(15*(sqrt(10*(417+(107*sqrt(5)))))))^(3/2))

Volume of Hexakis Icosahedron given Insphere Radius

Go Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((4*Insphere Radius of Hexakis Icosahedron)/(sqrt((15/241)*(275+(119*sqrt(5))))))^3)

Volume of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

Go Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(8/125)*(Truncated Edge of Hexakis Icosahedron^3)*((sqrt(15*(5-sqrt(5))))^3)

Volume of Hexakis Icosahedron given Medium Edge

Go Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))^3)

Volume of Hexakis Icosahedron given Short Edge

Go Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))^3)

Volume of Hexakis Icosahedron given Midsphere Radius

Go Volume of Hexakis Icosahedron = 25/88*((8*Midsphere Radius of Hexakis Icosahedron)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))

Volume of Hexakis Icosahedron

Go Volume of Hexakis Icosahedron = 25/88*Long Edge of Hexakis Icosahedron^3*sqrt(6*(185+82*sqrt(5)))

Volume of Hexakis Icosahedron given Midsphere Radius Formula

Volume of Hexakis Icosahedron = 25/88*((8*Midsphere Radius of Hexakis Icosahedron)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))
V = 25/88*((8*r_m)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5)))

What is Hexakis Icosahedron?

A Hexakis Icosahedron is a polyhedron with identical, but irregular triangle faces. It has thirty vertices with four edges, twenty vertices with six edges and twelve vertices with ten edges. It has 120 faces, 180 edges, 62 vertices.

How to Calculate Volume of Hexakis Icosahedron given Midsphere Radius?

Volume of Hexakis Icosahedron given Midsphere Radius calculator uses Volume of Hexakis Icosahedron = 25/88*((8*Midsphere Radius of Hexakis Icosahedron)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5))) to calculate the Volume of Hexakis Icosahedron, The Volume of Hexakis Icosahedron given Midsphere Radius formula is defined as the amount of three dimensional space covered by closed surface of Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron. Volume of Hexakis Icosahedron is denoted by V symbol.

How to calculate Volume of Hexakis Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Hexakis Icosahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Icosahedron (r_m) and hit the calculate button. Here is how the Volume of Hexakis Icosahedron given Midsphere Radius calculation can be explained with given input values -> 14379.4 = 25/88*((8*15)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5))).

FAQ

What is Volume of Hexakis Icosahedron given Midsphere Radius?

The Volume of Hexakis Icosahedron given Midsphere Radius formula is defined as the amount of three dimensional space covered by closed surface of Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron and is represented as V = 25/88*((8*r_m)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5))) or Volume of Hexakis Icosahedron = 25/88*((8*Midsphere Radius of Hexakis Icosahedron)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5))). Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

How to calculate Volume of Hexakis Icosahedron given Midsphere Radius?

The Volume of Hexakis Icosahedron given Midsphere Radius formula is defined as the amount of three dimensional space covered by closed surface of Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron is calculated using Volume of Hexakis Icosahedron = 25/88*((8*Midsphere Radius of Hexakis Icosahedron)/(5+3*sqrt(5)))^3*sqrt(6*(185+82*sqrt(5))). To calculate Volume of Hexakis Icosahedron given Midsphere Radius, you need Midsphere Radius of Hexakis Icosahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Hexakis Icosahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Hexakis Icosahedron?

In this formula, Volume of Hexakis Icosahedron uses Midsphere Radius of Hexakis Icosahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))^3)
Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(8/125)*(Truncated Edge of Hexakis Icosahedron^3)*((sqrt(15*(5-sqrt(5))))^3)
Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((44*Total Surface Area of Hexakis Icosahedron)/(15*(sqrt(10*(417+(107*sqrt(5)))))))^(3/2))
Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((4*Insphere Radius of Hexakis Icosahedron)/(sqrt((15/241)*(275+(119*sqrt(5))))))^3)
Volume of Hexakis Icosahedron = (25/88)*(sqrt(6*(185+(82*sqrt(5)))))*(((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))^3)
Volume of Hexakis Icosahedron = 25/88*Long Edge of Hexakis Icosahedron^3*sqrt(6*(185+82*sqrt(5)))
Volume of Hexakis Icosahedron = 25/88*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))^3*sqrt(6*(185+82*sqrt(5)))

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