Volume of Octahedron given Midsphere Radius Calculator

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

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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 Midsphere Radius [V]

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Volume of Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3
V = sqrt(2)/3*(2*r_m)^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 Octahedron - (Measured in Cubic Meter) - Volume of Octahedron is the total quantity of three dimensional space enclosed by the entire surface of the Octahedron.
Midsphere Radius of Octahedron - (Measured in Meter) - Midsphere Radius of Octahedron is the radius of the sphere for which all the edges of the Octahedron become a tangent line to that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Octahedron: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = sqrt(2)/3*(2*r_m)^3 --> sqrt(2)/3*(2*5)^3

Evaluating ... ...

V = 471.404520791032

STEP 3: Convert Result to Output's Unit

471.404520791032 Cubic Meter --> No Conversion Required

FINAL ANSWER

471.404520791032 ≈ 471.4045 Cubic Meter <-- Volume of Octahedron

(Calculation completed in 00.020 seconds)

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

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< Volume of Octahedron Calculators

Volume of Octahedron given Midsphere Radius

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

Volume of Octahedron given Insphere Radius

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

Volume of Octahedron

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

Volume of Octahedron given Circumsphere Radius

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

Volume of Octahedron given Midsphere Radius Formula

LaTeX Go

Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3
V = sqrt(2)/3*(2*r_m)^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 Midsphere Radius?

Volume of Octahedron given Midsphere Radius calculator uses Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3 to calculate the Volume of Octahedron, The Volume of Octahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the midsphere radius of the Octahedron. Volume of Octahedron is denoted by V symbol.

How to calculate Volume of Octahedron given Midsphere Radius using this online calculator? To use this online calculator for Volume of Octahedron given Midsphere Radius, enter Midsphere Radius of Octahedron (r_m) and hit the calculate button. Here is how the Volume of Octahedron given Midsphere Radius calculation can be explained with given input values -> 471.4045 = sqrt(2)/3*(2*5)^3.

FAQ

What is Volume of Octahedron given Midsphere Radius?

The Volume of Octahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the midsphere radius of the Octahedron and is represented as V = sqrt(2)/3*(2*r_m)^3 or Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3. Midsphere Radius of Octahedron is the radius of the sphere for which all the edges of the Octahedron become a tangent line to that sphere.

How to calculate Volume of Octahedron given Midsphere Radius?

The Volume of Octahedron given Midsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the midsphere radius of the Octahedron is calculated using Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3. To calculate Volume of Octahedron given Midsphere Radius, you need Midsphere Radius of Octahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Midsphere Radius of Octahedron. We can use 3 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

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