Volume of Stellated Octahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Stellated Octahedron is the radius of the sphere that contains the Stellated Octahedron in such a way that all the vertices are lying on sphere.ⓘ Circumsphere Radius of Stellated Octahedron [r_c]

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✖Volume of Stellated Octahedron is the total quantity of three dimensional space enclosed by the surface of the Stellated Octahedron.ⓘ Volume of Stellated Octahedron given Circumsphere Radius [V]

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Volume of Stellated Octahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Stellated Octahedron = (sqrt(2)/8)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^3)
V = (sqrt(2)/8)*((4*r_c/sqrt(6))^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 Stellated Octahedron - (Measured in Cubic Meter) - Volume of Stellated Octahedron is the total quantity of three dimensional space enclosed by the surface of the Stellated Octahedron.
Circumsphere Radius of Stellated Octahedron - (Measured in Meter) - Circumsphere Radius of Stellated Octahedron is the radius of the sphere that contains the Stellated Octahedron in such a way that all the vertices are lying on sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Stellated Octahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (sqrt(2)/8)*((4*r_c/sqrt(6))^3) --> (sqrt(2)/8)*((4*6/sqrt(6))^3)

Evaluating ... ...

V = 166.276877526612

STEP 3: Convert Result to Output's Unit

166.276877526612 Cubic Meter --> No Conversion Required

FINAL ANSWER

166.276877526612 ≈ 166.2769 Cubic Meter <-- Volume of Stellated Octahedron

(Calculation completed in 00.020 seconds)

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< Volume of Stellated Octahedron Calculators

Volume of Stellated Octahedron given Total Surface Area

LaTeX Go Volume of Stellated Octahedron = (sqrt(2)/8)*((2*Total Surface Area of Stellated Octahedron)/(3*sqrt(3)))^(3/2)

Volume of Stellated Octahedron given Circumsphere Radius

LaTeX Go Volume of Stellated Octahedron = (sqrt(2)/8)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^3)

Volume of Stellated Octahedron given Edge Length of Peaks

LaTeX Go Volume of Stellated Octahedron = (sqrt(2)/8)*(2*Edge Length of Peaks of Stellated Octahedron)^3

Volume of Stellated Octahedron

LaTeX Go Volume of Stellated Octahedron = (sqrt(2)/8)*Edge Length of Stellated Octahedron^3

Volume of Stellated Octahedron given Circumsphere Radius Formula

LaTeX Go

Volume of Stellated Octahedron = (sqrt(2)/8)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^3)
V = (sqrt(2)/8)*((4*r_c/sqrt(6))^3)

What is Stellated Octahedron?

The Stellated Octahedron is the only stellation of the octahedron. It is also called the stella octangula, a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers.
It is the simplest of five regular polyhedral compounds, and the only regular compound of two tetrahedra. It is also the least dense of the regular polyhedral compounds, having a density of 2.

How to Calculate Volume of Stellated Octahedron given Circumsphere Radius?

Volume of Stellated Octahedron given Circumsphere Radius calculator uses Volume of Stellated Octahedron = (sqrt(2)/8)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^3) to calculate the Volume of Stellated Octahedron, Volume of Stellated Octahedron given Circumsphere Radius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Stellated Octahedron, calculated using its circumsphere radius. Volume of Stellated Octahedron is denoted by V symbol.

How to calculate Volume of Stellated Octahedron given Circumsphere Radius using this online calculator? To use this online calculator for Volume of Stellated Octahedron given Circumsphere Radius, enter Circumsphere Radius of Stellated Octahedron (r_c) and hit the calculate button. Here is how the Volume of Stellated Octahedron given Circumsphere Radius calculation can be explained with given input values -> 166.2769 = (sqrt(2)/8)*((4*6/sqrt(6))^3).

FAQ

What is Volume of Stellated Octahedron given Circumsphere Radius?

Volume of Stellated Octahedron given Circumsphere Radius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Stellated Octahedron, calculated using its circumsphere radius and is represented as V = (sqrt(2)/8)*((4*r_c/sqrt(6))^3) or Volume of Stellated Octahedron = (sqrt(2)/8)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^3). Circumsphere Radius of Stellated Octahedron is the radius of the sphere that contains the Stellated Octahedron in such a way that all the vertices are lying on sphere.

How to calculate Volume of Stellated Octahedron given Circumsphere Radius?

Volume of Stellated Octahedron given Circumsphere Radius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Stellated Octahedron, calculated using its circumsphere radius is calculated using Volume of Stellated Octahedron = (sqrt(2)/8)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^3). To calculate Volume of Stellated Octahedron given Circumsphere Radius, you need Circumsphere Radius of Stellated Octahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Stellated 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 Stellated Octahedron?

In this formula, Volume of Stellated Octahedron uses Circumsphere Radius of Stellated Octahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Stellated Octahedron = (sqrt(2)/8)*Edge Length of Stellated Octahedron^3
Volume of Stellated Octahedron = (sqrt(2)/8)*(2*Edge Length of Peaks of Stellated Octahedron)^3
Volume of Stellated Octahedron = (sqrt(2)/8)*((2*Total Surface Area of Stellated Octahedron)/(3*sqrt(3)))^(3/2)

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