Total Surface Area of Stellated Octahedron given Circumsphere Radius Calculator

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

+10%

-10%

✖Total Surface Area of Stellated Octahedron is the total quantity of plane enclosed on the entire surface of the Stellated Octahedron.ⓘ Total Surface Area of Stellated Octahedron given Circumsphere Radius [TSA]

⎘ Copy

👎

Formula

✖

Total Surface Area of Stellated Octahedron given Circumsphere Radius

Formula

`"TSA" = (3/2)*sqrt(3)*((4*"r"_{"c"}/sqrt(6))^2)`

Example

`"249.4153m²"=(3/2)*sqrt(3)*((4*"6m"/sqrt(6))^2)`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Total Surface Area of Stellated Octahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^2)
TSA = (3/2)*sqrt(3)*((4*r_c/sqrt(6))^2)
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

Total Surface Area of Stellated Octahedron - (Measured in Square Meter) - Total Surface Area of Stellated Octahedron is the total quantity of plane enclosed on the entire surface of the Stellated Octahedron.
Circumsphere Radius of Stellated Octahedron - (Measured in Meter) - Circumsphere Radius of Stellated Octahedron is the radius of the sphere that contains the Stellated Octahedron in such a way that all the vertices are lying on sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Stellated Octahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (3/2)*sqrt(3)*((4*r_c/sqrt(6))^2) --> (3/2)*sqrt(3)*((4*6/sqrt(6))^2)

Evaluating ... ...

TSA = 249.415316289918

STEP 3: Convert Result to Output's Unit

249.415316289918 Square Meter --> No Conversion Required

FINAL ANSWER

249.415316289918 ≈ 249.4153 Square Meter <-- Total Surface Area of Stellated Octahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Stellated Octahedron » Surface Area of Stellated Octahedron » Total Surface Area of Stellated Octahedron » Total Surface Area of Stellated Octahedron given Circumsphere Radius

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 5 Total Surface Area of Stellated Octahedron Calculators

Total Surface Area of Stellated Octahedron given Surface to Volume Ratio

Go Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((((3/2)*sqrt(3))/((1/8)*sqrt(2)*Surface to Volume Ratio of Stellated Octahedron))^2)

Total Surface Area of Stellated Octahedron given Circumsphere Radius

Go Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^2)

Total Surface Area of Stellated Octahedron given Volume

Go Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((8*Volume of Stellated Octahedron/sqrt(2))^(2/3))

Total Surface Area of Stellated Octahedron given Edge Length of Peaks

Go Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((2*Edge Length of Peaks of Stellated Octahedron)^2)

Total Surface Area of Stellated Octahedron

Go Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*Edge Length of Stellated Octahedron^2

Total Surface Area of Stellated Octahedron given Circumsphere Radius Formula

Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^2)
TSA = (3/2)*sqrt(3)*((4*r_c/sqrt(6))^2)

What is Stellated Octahedron?

The Stellated Octahedron is the only stellation of the octahedron. It is also called the stella octangula, a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers.
It is the simplest of five regular polyhedral compounds, and the only regular compound of two tetrahedra. It is also the least dense of the regular polyhedral compounds, having a density of 2.

How to Calculate Total Surface Area of Stellated Octahedron given Circumsphere Radius?

Total Surface Area of Stellated Octahedron given Circumsphere Radius calculator uses Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^2) to calculate the Total Surface Area of Stellated Octahedron, Total Surface Area of Stellated Octahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Stellated Octahedron, calculated using its circumsphere radius. Total Surface Area of Stellated Octahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Stellated Octahedron given Circumsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Stellated Octahedron given Circumsphere Radius, enter Circumsphere Radius of Stellated Octahedron (r_c) and hit the calculate button. Here is how the Total Surface Area of Stellated Octahedron given Circumsphere Radius calculation can be explained with given input values -> 249.4153 = (3/2)*sqrt(3)*((4*6/sqrt(6))^2).

FAQ

What is Total Surface Area of Stellated Octahedron given Circumsphere Radius?

Total Surface Area of Stellated Octahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Stellated Octahedron, calculated using its circumsphere radius and is represented as TSA = (3/2)*sqrt(3)*((4*r_c/sqrt(6))^2) or Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^2). Circumsphere Radius of Stellated Octahedron is the radius of the sphere that contains the Stellated Octahedron in such a way that all the vertices are lying on sphere.

How to calculate Total Surface Area of Stellated Octahedron given Circumsphere Radius?

Total Surface Area of Stellated Octahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Stellated Octahedron, calculated using its circumsphere radius is calculated using Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((4*Circumsphere Radius of Stellated Octahedron/sqrt(6))^2). To calculate Total Surface Area of Stellated Octahedron given Circumsphere Radius, you need Circumsphere Radius of Stellated Octahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Stellated 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 Total Surface Area of Stellated Octahedron?

In this formula, Total Surface Area of Stellated Octahedron uses Circumsphere Radius of Stellated Octahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*Edge Length of Stellated Octahedron^2
Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((2*Edge Length of Peaks of Stellated Octahedron)^2)
Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((8*Volume of Stellated Octahedron/sqrt(2))^(2/3))
Total Surface Area of Stellated Octahedron = (3/2)*sqrt(3)*((((3/2)*sqrt(3))/((1/8)*sqrt(2)*Surface to Volume Ratio of Stellated Octahedron))^2)

Home

FREE PDFs

🔍 Search