Volume of Octahedron given Insphere Radius Calculator

✖Insphere Radius of Octahedron is the radius of the sphere that is contained by the Octahedron in such a way that all the faces are just touching the sphere.ⓘ Insphere Radius of Octahedron [r_i]

+10%

-10%

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

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Octahedron Formula PDF PDF Image

Volume of Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3
V = 4*sqrt(3)*r_i^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.
Insphere Radius of Octahedron - (Measured in Meter) - Insphere Radius of Octahedron is the radius of the sphere that is contained by the Octahedron in such a way that all the faces are just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Octahedron: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 4*sqrt(3)*r_i^3 --> 4*sqrt(3)*4^3

Evaluating ... ...

V = 443.405006737633

STEP 3: Convert Result to Output's Unit

443.405006737633 Cubic Meter --> No Conversion Required

FINAL ANSWER

443.405006737633 ≈ 443.405 Cubic Meter <-- Volume of Octahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Platonic Solids » Octahedron » Volume of Octahedron » Volume of Octahedron given Insphere Radius

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 1100+ more calculators!

< 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 Calculators

Volume of Octahedron given Total Surface Area

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

LaTeX Go

Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3
V = 4*sqrt(3)*r_i^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 Insphere Radius?

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

How to calculate Volume of Octahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Octahedron given Insphere Radius, enter Insphere Radius of Octahedron (r_i) and hit the calculate button. Here is how the Volume of Octahedron given Insphere Radius calculation can be explained with given input values -> 443.405 = 4*sqrt(3)*4^3.

FAQ

What is Volume of Octahedron given Insphere Radius?

Volume of Octahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron, and calculated using insphere radius of the Octahedron and is represented as V = 4*sqrt(3)*r_i^3 or Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3. Insphere Radius of Octahedron is the radius of the sphere that is contained by the Octahedron in such a way that all the faces are just touching the sphere.

How to calculate Volume of Octahedron given Insphere Radius?

Volume of Octahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron, and calculated using insphere radius of the Octahedron is calculated using Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3. To calculate Volume of Octahedron given Insphere Radius, you need Insphere Radius of Octahedron (r_i). With our tool, you need to enter the respective value for Insphere 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 Insphere 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*Circumsphere Radius of Octahedron^3)/3
Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3

Home

FREE PDFs

🔍 Search