Volume of Octahedron given Space Diagonal Calculator

✖The Space Diagonal of Octahedron is the line connecting two vertices that are not on the same face of Octahedron.ⓘ Space Diagonal of Octahedron [d_Space]

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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 Space Diagonal [V]

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Formula

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Volume of Octahedron given Space Diagonal

Formula

`"V" = ("d"_{"Space"}^3)/(6)`

Example

`"457.3333m³"=(("14m")^3)/(6)`

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Volume of Octahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Octahedron = (Space Diagonal of Octahedron^3)/(6)
V = (d_Space^3)/(6)
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.
Space Diagonal of Octahedron - (Measured in Meter) - The Space Diagonal of Octahedron is the line connecting two vertices that are not on the same face of Octahedron.

STEP 1: Convert Input(s) to Base Unit

Space Diagonal of Octahedron: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (d_Space^3)/(6) --> (14^3)/(6)

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 00.004 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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< 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)

Volume of Octahedron given Space Diagonal Formula

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

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 Space Diagonal?

Volume of Octahedron given Space Diagonal calculator uses Volume of Octahedron = (Space Diagonal of Octahedron^3)/(6) to calculate the Volume of Octahedron, The Volume of Octahedron given Space Diagonal formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the space diagonal of the Octahedron. Volume of Octahedron is denoted by V symbol.

How to calculate Volume of Octahedron given Space Diagonal using this online calculator? To use this online calculator for Volume of Octahedron given Space Diagonal, enter Space Diagonal of Octahedron (d_Space) and hit the calculate button. Here is how the Volume of Octahedron given Space Diagonal calculation can be explained with given input values -> 457.3333 = (14^3)/(6).

FAQ

What is Volume of Octahedron given Space Diagonal?

The Volume of Octahedron given Space Diagonal formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the space diagonal of the Octahedron and is represented as V = (d_Space^3)/(6) or Volume of Octahedron = (Space Diagonal of Octahedron^3)/(6). The Space Diagonal of Octahedron is the line connecting two vertices that are not on the same face of Octahedron.

How to calculate Volume of Octahedron given Space Diagonal?

The Volume of Octahedron given Space Diagonal formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the space diagonal of the Octahedron is calculated using Volume of Octahedron = (Space Diagonal of Octahedron^3)/(6). To calculate Volume of Octahedron given Space Diagonal, you need Space Diagonal of Octahedron (d_Space). With our tool, you need to enter the respective value for Space Diagonal 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 Space Diagonal of Octahedron. We can use 6 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 = (4*Circumsphere Radius of Octahedron^3)/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

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