Volume of Hexakis Octahedron given Midsphere Radius Calculator

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

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

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Formula

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Volume of Hexakis Octahedron given Midsphere Radius

Formula

`"V" = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*"r"_{"m"})/(1+(2*sqrt(2))))^3)`

Example

`"29391.92m³"=((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*"19m")/(1+(2*sqrt(2))))^3)`

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Volume of Hexakis Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^3)
V = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*r_m)/(1+(2*sqrt(2))))^3)
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 Octahedron - (Measured in Cubic Meter) - Volume of Hexakis Octahedron is the quantity of three dimensional space enclosed by the entire surface of Hexakis Octahedron.
Midsphere Radius of Hexakis Octahedron - (Measured in Meter) - Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Hexakis Octahedron: 19 Meter --> 19 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*r_m)/(1+(2*sqrt(2))))^3) --> ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*19)/(1+(2*sqrt(2))))^3)

Evaluating ... ...

V = 29391.9247410904

STEP 3: Convert Result to Output's Unit

29391.9247410904 Cubic Meter --> No Conversion Required

FINAL ANSWER

29391.9247410904 ≈ 29391.92 Cubic Meter <-- Volume of Hexakis Octahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 8 Volume of Hexakis Octahedron Calculators

Volume of Hexakis Octahedron given Surface to Volume Ratio

Go Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*sqrt(6*(986+(607*sqrt(2))))))^3)

Volume of Hexakis Octahedron given Total Surface Area

Go Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2)))))^(3/2))

Volume of Hexakis Octahedron given Insphere Radius

Go Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))^3)

Volume of Hexakis Octahedron given Truncated Cuboctahedron Edge

Go Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(8/343)*((60+(6*sqrt(2)))^(3/2))*(Truncated Cuboctahedron Edge of Hexakis Octahedron^3)

Volume of Hexakis Octahedron given Midsphere Radius

Go Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^3)

Volume of Hexakis Octahedron given Medium Edge

Go Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))^3)

Volume of Hexakis Octahedron given Short Edge

Go Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))^3)

Volume of Hexakis Octahedron

Go Volume of Hexakis Octahedron = (((Long Edge of Hexakis Octahedron)^3)*(sqrt(6*(986+(607*sqrt(2))))))/28

Volume of Hexakis Octahedron given Midsphere Radius Formula

Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^3)
V = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*r_m)/(1+(2*sqrt(2))))^3)

What is Hexakis Octahedron?

In geometry, a Hexakis Octahedron (also called hexoctahedron, disdyakis dodecahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 congruent triangular faces, 72 edges and 26 vertices. It is the dual of the Archimedean solid ‘truncated cuboctahedron’. As such it is face-transitive but with irregular face polygons.

How to Calculate Volume of Hexakis Octahedron given Midsphere Radius?

Volume of Hexakis Octahedron given Midsphere Radius calculator uses Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^3) to calculate the Volume of Hexakis Octahedron, The Volume of Hexakis Octahedron given Midsphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron. Volume of Hexakis Octahedron is denoted by V symbol.

How to calculate Volume of Hexakis Octahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Hexakis Octahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Octahedron (r_m) and hit the calculate button. Here is how the Volume of Hexakis Octahedron given Midsphere Radius calculation can be explained with given input values -> 29391.92 = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*19)/(1+(2*sqrt(2))))^3).

FAQ

What is Volume of Hexakis Octahedron given Midsphere Radius?

The Volume of Hexakis Octahedron given Midsphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron and is represented as V = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*r_m)/(1+(2*sqrt(2))))^3) or Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^3). Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere.

How to calculate Volume of Hexakis Octahedron given Midsphere Radius?

The Volume of Hexakis Octahedron given Midsphere Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron is calculated using Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^3). To calculate Volume of Hexakis Octahedron given Midsphere Radius, you need Midsphere Radius of Hexakis Octahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Hexakis Octahedron 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 Octahedron?

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

Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))^3)
Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))^3)
Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))^3)
Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2)))))^(3/2))
Volume of Hexakis Octahedron = (((Long Edge of Hexakis Octahedron)^3)*(sqrt(6*(986+(607*sqrt(2))))))/28
Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(8/343)*((60+(6*sqrt(2)))^(3/2))*(Truncated Cuboctahedron Edge of Hexakis Octahedron^3)
Volume of Hexakis Octahedron = ((sqrt(6*(986+(607*sqrt(2)))))/28)*(((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*sqrt(6*(986+(607*sqrt(2))))))^3)

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