Volume of Octahedron given Circumsphere Radius Calculator

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

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

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Formula

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Volume of Octahedron given Circumsphere Radius

Formula

`"V" = (4*"r"_{"c"}^3)/3`

Example

`"457.3333m³"=(4*("7m")^3)/3`

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Volume of Octahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Octahedron = (4*Circumsphere Radius of Octahedron^3)/3
V = (4*r_c^3)/3
This formula uses 2 Variables

Variables Used

Volume of Octahedron - (Measured in Cubic Meter) - Volume of Octahedron is the total quantity of three dimensional space enclosed by the entire surface of the Octahedron.
Circumsphere Radius of Octahedron - (Measured in Meter) - Circumsphere Radius of Octahedron is the radius of the sphere that contains the Octahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Octahedron: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (4*r_c^3)/3 --> (4*7^3)/3

Evaluating ... ...

V = 457.333333333333

STEP 3: Convert Result to Output's Unit

457.333333333333 Cubic Meter --> No Conversion Required

FINAL ANSWER

457.333333333333 ≈ 457.3333 Cubic Meter <-- Volume of Octahedron

(Calculation completed in 00.006 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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Mumbai University (DJSCE), Mumbai

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< 7 Volume of Octahedron Calculators

Volume of Octahedron given Total Surface Area

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

Volume of Octahedron given Surface to Volume Ratio

Go Volume of Octahedron = sqrt(2)/3*((3*sqrt(6))/Surface to Volume Ratio of Octahedron)^3

Volume of Octahedron given Midsphere Radius

Go Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3

Volume of Octahedron given Insphere Radius

Go Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3

Volume of Octahedron

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

Volume of Octahedron given Circumsphere Radius

Go Volume of Octahedron = (4*Circumsphere Radius of Octahedron^3)/3

Volume of Octahedron given Space Diagonal

Go Volume of Octahedron = (Space Diagonal of Octahedron^3)/(6)

< 4 Volume of Octahedron Calculators

Volume of Octahedron given Total Surface Area

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

Volume of Octahedron given Insphere Radius

Go Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3

Volume of Octahedron

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

Volume of Octahedron given Circumsphere Radius

Go Volume of Octahedron = (4*Circumsphere Radius of Octahedron^3)/3

Volume of Octahedron given Circumsphere Radius Formula

Volume of Octahedron = (4*Circumsphere Radius of Octahedron^3)/3
V = (4*r_c^3)/3

What is an Octahedron?

An Octahedron is a symmetric and closed three dimensional shape with 8 identical equilateral triangular faces. It is a Platonic solid, which has 8 faces, 6 vertices and 12 edges. At each vertex, four equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Volume of Octahedron given Circumsphere Radius?

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

How to calculate Volume of Octahedron given Circumsphere Radius using this online calculator? To use this online calculator for Volume of Octahedron given Circumsphere Radius, enter Circumsphere Radius of Octahedron (r_c) and hit the calculate button. Here is how the Volume of Octahedron given Circumsphere Radius calculation can be explained with given input values -> 457.3333 = (4*7^3)/3.

FAQ

What is Volume of Octahedron given Circumsphere Radius?

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

How to calculate Volume of Octahedron given Circumsphere Radius?

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

In this formula, Volume of Octahedron uses Circumsphere Radius of Octahedron. We can use 9 other way(s) to calculate the same, which is/are as follows -

Volume of Octahedron = sqrt(2)/3*Edge Length of Octahedron^3
Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3
Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3
Volume of Octahedron = sqrt(2)/3*((3*sqrt(6))/Surface to Volume Ratio of Octahedron)^3
Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3
Volume of Octahedron = (Space Diagonal of Octahedron^3)/(6)
Volume of Octahedron = sqrt(2)/3*Edge Length of Octahedron^3
Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3
Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3

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