Total Surface Area of Hexakis Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^2)
TSA = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*rm)/(1+(2*sqrt(2))))^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 Hexakis Octahedron - (Measured in Square Meter) - Total Surface Area of Hexakis Octahedron is the amount or quantity of two dimensional space covered on the surface of Hexakis Octahedron.
Midsphere Radius of Hexakis Octahedron - (Measured in Meter) - Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Hexakis Octahedron: 19 Meter --> 19 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*rm)/(1+(2*sqrt(2))))^2) --> (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*19)/(1+(2*sqrt(2))))^2)
Evaluating ... ...
TSA = 4752.75291353267
STEP 3: Convert Result to Output's Unit
4752.75291353267 Square Meter --> No Conversion Required
FINAL ANSWER
4752.75291353267 4752.753 Square Meter <-- Total Surface Area of Hexakis Octahedron
(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli
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8 Total Surface Area of Hexakis Octahedron Calculators

Total Surface Area of Hexakis Octahedron given Surface to Volume Ratio
Go Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((12*(sqrt(543+(176*sqrt(2)))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2)))))))^2)
Total Surface Area of Hexakis Octahedron given Volume
Go Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(2/3))
Total Surface Area of Hexakis Octahedron given Truncated Cuboctahedron Edge
Go Total Surface Area of Hexakis Octahedron = (3/7)*(4/49)*(sqrt(543+(176*sqrt(2))))*(60+(6*sqrt(2)))*(Truncated Cuboctahedron Edge of Hexakis Octahedron^2)
Total Surface Area of Hexakis Octahedron given Insphere Radius
Go Total Surface Area of Hexakis Octahedron = (12/7)*(sqrt(543+(176*sqrt(2))))*((Insphere Radius of Hexakis Octahedron)^2)*(1/((402+(195*sqrt(2)))/194))
Total Surface Area of Hexakis Octahedron given Midsphere Radius
Go Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^2)
Total Surface Area of Hexakis Octahedron given Medium Edge
Go Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))^2)
Total Surface Area of Hexakis Octahedron given Short Edge
Go Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))^2)
Total Surface Area of Hexakis Octahedron
Go Total Surface Area of Hexakis Octahedron = ((Long Edge of Hexakis Octahedron)^2)*(sqrt(543+(176*sqrt(2))))*(3/7)

Total Surface Area of Hexakis Octahedron given Midsphere Radius Formula

Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^2)
TSA = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*rm)/(1+(2*sqrt(2))))^2)

What is Hexakis Octahedron?

In geometry, a Hexakis Octahedron (also called hexoctahedron, disdyakis dodecahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 congruent triangular faces, 72 edges and 26 vertices. It is the dual of the Archimedean solid ‘truncated cuboctahedron’. As such it is face-transitive but with irregular face polygons.

How to Calculate Total Surface Area of Hexakis Octahedron given Midsphere Radius?

Total Surface Area of Hexakis Octahedron given Midsphere Radius calculator uses Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^2) to calculate the Total Surface Area of Hexakis Octahedron, The Total Surface Area of Hexakis Octahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron. Total Surface Area of Hexakis Octahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Hexakis Octahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Hexakis Octahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Octahedron (rm) and hit the calculate button. Here is how the Total Surface Area of Hexakis Octahedron given Midsphere Radius calculation can be explained with given input values -> 4752.753 = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*19)/(1+(2*sqrt(2))))^2).

FAQ

What is Total Surface Area of Hexakis Octahedron given Midsphere Radius?
The Total Surface Area of Hexakis Octahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron and is represented as TSA = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*rm)/(1+(2*sqrt(2))))^2) or Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^2). Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere.
How to calculate Total Surface Area of Hexakis Octahedron given Midsphere Radius?
The Total Surface Area of Hexakis Octahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron is calculated using Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))^2). To calculate Total Surface Area of Hexakis Octahedron given Midsphere Radius, you need Midsphere Radius of Hexakis Octahedron (rm). With our tool, you need to enter the respective value for Midsphere Radius of Hexakis 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 Hexakis Octahedron?
In this formula, Total Surface Area of Hexakis Octahedron uses Midsphere Radius of Hexakis Octahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Hexakis Octahedron = ((Long Edge of Hexakis Octahedron)^2)*(sqrt(543+(176*sqrt(2))))*(3/7)
  • Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))^2)
  • Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))^2)
  • Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(2/3))
  • Total Surface Area of Hexakis Octahedron = (12/7)*(sqrt(543+(176*sqrt(2))))*((Insphere Radius of Hexakis Octahedron)^2)*(1/((402+(195*sqrt(2)))/194))
  • Total Surface Area of Hexakis Octahedron = (3/7)*(sqrt(543+(176*sqrt(2))))*(((12*(sqrt(543+(176*sqrt(2)))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2)))))))^2)
  • Total Surface Area of Hexakis Octahedron = (3/7)*(4/49)*(sqrt(543+(176*sqrt(2))))*(60+(6*sqrt(2)))*(Truncated Cuboctahedron Edge of Hexakis Octahedron^2)
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