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*rc/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*rc/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)

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Walchand College of Engineering (WCE), Sangli
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Indian Institute of Information Technology (IIIT), Bhopal
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Total Surface Area of Stellated Octahedron Calculators

Total Surface Area of Stellated Octahedron given Circumsphere Radius
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ 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

​LaTeX ​Go
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*rc/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 (rc) 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*rc/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 (rc). 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 3 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))
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