Total Surface Area 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]

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

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Total Surface Area of Triakis Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Triakis Octahedron = ((204*Insphere Radius of Triakis Octahedron^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2)))
TSA = ((204*r_i^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(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 Triakis Octahedron - (Measured in Square Meter) - Total Surface Area of Triakis Octahedron is the total quantity of plane enclosed on 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

TSA = ((204*r_i^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2))) --> ((204*4^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2)))

Evaluating ... ...

TSA = 254.499630329958

STEP 3: Convert Result to Output's Unit

254.499630329958 Square Meter --> No Conversion Required

FINAL ANSWER

254.499630329958 ≈ 254.4996 Square Meter <-- Total Surface Area of Triakis Octahedron

(Calculation completed in 00.021 seconds)

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< Surface Area of Triakis Octahedron Calculators

Total Surface Area of Triakis Octahedron given Surface to Volume Ratio

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

Total Surface Area of Triakis Octahedron given Insphere Radius

LaTeX Go Total Surface Area of Triakis Octahedron = ((204*Insphere Radius of Triakis Octahedron^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2)))

Total Surface Area of Triakis Octahedron given Volume

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

Total Surface Area of Triakis Octahedron given Midsphere Radius

LaTeX Go Total Surface Area of Triakis Octahedron = 6*(2*Midsphere Radius of Triakis Octahedron)^2*sqrt(23-(16*sqrt(2)))

Total Surface Area of Triakis Octahedron given Insphere Radius Formula

LaTeX Go

Total Surface Area of Triakis Octahedron = ((204*Insphere Radius of Triakis Octahedron^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2)))
TSA = ((204*r_i^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2)))

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 Total Surface Area of Triakis Octahedron given Insphere Radius?

Total Surface Area of Triakis Octahedron given Insphere Radius calculator uses Total Surface Area of Triakis Octahedron = ((204*Insphere Radius of Triakis Octahedron^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2))) to calculate the Total Surface Area of Triakis Octahedron, The Total Surface Area of Triakis Octahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Triakis Octahedron, calculated using the insphere radius of the Triakis Octahedron. Total Surface Area of Triakis Octahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Triakis Octahedron given Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Triakis Octahedron given Insphere Radius, enter Insphere Radius of Triakis Octahedron (r_i) and hit the calculate button. Here is how the Total Surface Area of Triakis Octahedron given Insphere Radius calculation can be explained with given input values -> 254.4996 = ((204*4^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2))).

FAQ

What is Total Surface Area of Triakis Octahedron given Insphere Radius?

The Total Surface Area of Triakis Octahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Triakis Octahedron, calculated using the insphere radius of the Triakis Octahedron and is represented as TSA = ((204*r_i^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2))) or Total Surface Area of Triakis Octahedron = ((204*Insphere Radius of Triakis Octahedron^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2))). 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 Total Surface Area of Triakis Octahedron given Insphere Radius?

The Total Surface Area of Triakis Octahedron given Insphere Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Triakis Octahedron, calculated using the insphere radius of the Triakis Octahedron is calculated using Total Surface Area of Triakis Octahedron = ((204*Insphere Radius of Triakis Octahedron^2)/(5+(2*sqrt(2))))*sqrt(23-(16*sqrt(2))). To calculate Total Surface Area 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 Total Surface Area of Triakis Octahedron?

In this formula, Total Surface Area of Triakis Octahedron uses Insphere Radius of Triakis Octahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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