Volume of Triakis Octahedron given Insphere Radius Calculator

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

+10%

-10%

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

⎘ Copy

👎

Formula

✖

Volume of Triakis Octahedron given Insphere Radius

Formula

`"V" = (2-sqrt(2))*(("r"_{"i"})/(sqrt((5+(2*sqrt(2)))/34)))^3`

Example

`"339.3328m³"=(2-sqrt(2))*(("4m")/(sqrt((5+(2*sqrt(2)))/34)))^3`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF PDF Image

Volume of Triakis Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Triakis Octahedron = (2-sqrt(2))*((Insphere Radius of Triakis Octahedron)/(sqrt((5+(2*sqrt(2)))/34)))^3
V = (2-sqrt(2))*((r_i)/(sqrt((5+(2*sqrt(2)))/34)))^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 Triakis Octahedron - (Measured in Cubic Meter) - Volume of Triakis Octahedron is the quantity of three-dimensional space enclosed by the entire surface of the Triakis Octahedron.
Insphere Radius of Triakis Octahedron - (Measured in Meter) - Insphere Radius of Triakis Octahedron is the radius of the sphere that is contained by the Triakis Octahedron in such a way that all the faces are touching the sphere.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (2-sqrt(2))*((r_i)/(sqrt((5+(2*sqrt(2)))/34)))^3 --> (2-sqrt(2))*((4)/(sqrt((5+(2*sqrt(2)))/34)))^3

Evaluating ... ...

V = 339.332840439944

STEP 3: Convert Result to Output's Unit

339.332840439944 Cubic Meter --> No Conversion Required

FINAL ANSWER

339.332840439944 ≈ 339.3328 Cubic Meter <-- Volume of Triakis Octahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » CatalanSolids » Triakis Octahedron » Volume of Triakis Octahedron » Volume of Triakis Octahedron given Insphere Radius

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

Nishan Poojary has verified this Calculator and 400+ more calculators!

< 6 Volume of Triakis Octahedron Calculators

Volume of Triakis Octahedron given Surface to Volume Ratio

Go Volume of Triakis Octahedron = (2-sqrt(2))*((6*sqrt(23-(16*sqrt(2))))/((2-sqrt(2))*Surface to Volume Ratio of Triakis Octahedron))^3

Volume of Triakis Octahedron given Total Surface Area

Go Volume of Triakis Octahedron = (2-sqrt(2))*((Total Surface Area of Triakis Octahedron)/(6*sqrt(23-(16*sqrt(2)))))^(3/2)

Volume of Triakis Octahedron given Insphere Radius

Go Volume of Triakis Octahedron = (2-sqrt(2))*((Insphere Radius of Triakis Octahedron)/(sqrt((5+(2*sqrt(2)))/34)))^3

Volume of Triakis Octahedron given Pyramidal Edge Length

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

Volume of Triakis Octahedron

Go Volume of Triakis Octahedron = (2-sqrt(2))*Octahedral Edge Length of Triakis Octahedron^3

Volume of Triakis Octahedron given Midsphere Radius

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

Volume of Triakis Octahedron given Insphere Radius Formula

Volume of Triakis Octahedron = (2-sqrt(2))*((Insphere Radius of Triakis Octahedron)/(sqrt((5+(2*sqrt(2)))/34)))^3
V = (2-sqrt(2))*((r_i)/(sqrt((5+(2*sqrt(2)))/34)))^3

What is Triakis Octahedron?

In geometry, a Triakis Octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube. It is a regular octahedron with matching regular triangular pyramids attached to its faces. It has eight vertices with three edges and six vertices with eight edges. Triakis Octahedron has 24 faces, 36 edges and 14 vertices.

How to Calculate Volume of Triakis Octahedron given Insphere Radius?

Volume of Triakis Octahedron given Insphere Radius calculator uses Volume of Triakis Octahedron = (2-sqrt(2))*((Insphere Radius of Triakis Octahedron)/(sqrt((5+(2*sqrt(2)))/34)))^3 to calculate the Volume of Triakis Octahedron, The Volume of Triakis Octahedron given Insphere Radius formula is defined as the quantity of three-dimensional space enclosed by the entire surface of the Triakis Octahedron, calculated using the insphere radius of Triakis Octahedron. Volume of Triakis Octahedron is denoted by V symbol.

How to calculate Volume of Triakis Octahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Triakis Octahedron given Insphere Radius, enter Insphere Radius of Triakis Octahedron (r_i) and hit the calculate button. Here is how the Volume of Triakis Octahedron given Insphere Radius calculation can be explained with given input values -> 339.3328 = (2-sqrt(2))*((4)/(sqrt((5+(2*sqrt(2)))/34)))^3.

FAQ

What is Volume of Triakis Octahedron given Insphere Radius?

The Volume of Triakis Octahedron given Insphere Radius formula is defined as the quantity of three-dimensional space enclosed by the entire surface of the Triakis Octahedron, calculated using the insphere radius of Triakis Octahedron and is represented as V = (2-sqrt(2))*((r_i)/(sqrt((5+(2*sqrt(2)))/34)))^3 or Volume of Triakis Octahedron = (2-sqrt(2))*((Insphere Radius of Triakis Octahedron)/(sqrt((5+(2*sqrt(2)))/34)))^3. Insphere Radius of Triakis Octahedron is the radius of the sphere that is contained by the Triakis Octahedron in such a way that all the faces are touching the sphere.

How to calculate Volume of Triakis Octahedron given Insphere Radius?

The Volume of Triakis Octahedron given Insphere Radius formula is defined as the quantity of three-dimensional space enclosed by the entire surface of the Triakis Octahedron, calculated using the insphere radius of Triakis Octahedron is calculated using Volume of Triakis Octahedron = (2-sqrt(2))*((Insphere Radius of Triakis Octahedron)/(sqrt((5+(2*sqrt(2)))/34)))^3. To calculate Volume of Triakis Octahedron given Insphere Radius, you need Insphere Radius of Triakis Octahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Triakis 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 Triakis Octahedron?

In this formula, Volume of Triakis Octahedron uses Insphere Radius of Triakis Octahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Volume of Triakis Octahedron = (2-sqrt(2))*Octahedral Edge Length of Triakis Octahedron^3
Volume of Triakis Octahedron = (2-sqrt(2))*((Pyramidal Edge Length of Triakis Octahedron)/(2-sqrt(2)))^3
Volume of Triakis Octahedron = (2-sqrt(2))*((Total Surface Area of Triakis Octahedron)/(6*sqrt(23-(16*sqrt(2)))))^(3/2)
Volume of Triakis Octahedron = (2-sqrt(2))*(2*Midsphere Radius of Triakis Octahedron)^3
Volume of Triakis Octahedron = (2-sqrt(2))*((6*sqrt(23-(16*sqrt(2))))/((2-sqrt(2))*Surface to Volume Ratio of Triakis Octahedron))^3

Home

FREE PDFs

🔍 Search