Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/Surface to Volume Ratio of Hexakis Icosahedron)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))
ri = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/RA/V)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))
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
Insphere Radius of Hexakis Icosahedron - (Measured in Meter) - Insphere Radius of Hexakis Icosahedron is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touching the sphere.
Surface to Volume Ratio of Hexakis Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Hexakis Icosahedron is what part of or fraction of total volume of Hexakis Icosahedron is the total surface area.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Hexakis Icosahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/RA/V)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5)))))) --> ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/0.2)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))
Evaluating ... ...
ri = 15
STEP 3: Convert Result to Output's Unit
15 Meter --> No Conversion Required
FINAL ANSWER
15 Meter <-- Insphere Radius of Hexakis Icosahedron
(Calculation completed in 00.004 seconds)

Credits

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Walchand College of Engineering (WCE), Sangli
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8 Insphere Radius of Hexakis Icosahedron Calculators

Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/Surface to Volume Ratio of Hexakis Icosahedron)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))
Insphere Radius of Hexakis Icosahedron given Total Surface Area
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(sqrt((44*Total Surface Area of Hexakis Icosahedron)/(15*(sqrt(10*(417+(107*sqrt(5))))))))
Insphere Radius of Hexakis Icosahedron given Volume
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(((88*Volume of Hexakis Icosahedron)/(25*(sqrt(6*(185+(82*sqrt(5)))))))^(1/3))
Insphere Radius of Hexakis Icosahedron given Truncated Icosidodecahedron Edge
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))
Insphere Radius of Hexakis Icosahedron given Midsphere Radius
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))
Insphere Radius of Hexakis Icosahedron given Medium Edge
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))
Insphere Radius of Hexakis Icosahedron given Short Edge
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))
Insphere Radius of Hexakis Icosahedron
Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*Long Edge of Hexakis Icosahedron

Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Formula

Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/Surface to Volume Ratio of Hexakis Icosahedron)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))
ri = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/RA/V)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))

What is Hexakis Icosahedron?

A Hexakis Icosahedron is a polyhedron with identical, but irregular triangle faces. It has thirty vertices with four edges, twenty vertices with six edges and twelve vertices with ten edges.
It has 120 faces, 180 edges, 62 vertices.

How to Calculate Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?

Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio calculator uses Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/Surface to Volume Ratio of Hexakis Icosahedron)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5)))))) to calculate the Insphere Radius of Hexakis Icosahedron, Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touch the sphere, calculated using surface to volume ratio of Hexakis Icosahedron. Insphere Radius of Hexakis Icosahedron is denoted by ri symbol.

How to calculate Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Hexakis Icosahedron (RA/V) and hit the calculate button. Here is how the Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 15 = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/0.2)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5)))))).

FAQ

What is Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?
Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touch the sphere, calculated using surface to volume ratio of Hexakis Icosahedron and is represented as ri = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/RA/V)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5)))))) or Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/Surface to Volume Ratio of Hexakis Icosahedron)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5)))))). Surface to Volume Ratio of Hexakis Icosahedron is what part of or fraction of total volume of Hexakis Icosahedron is the total surface area.
How to calculate Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?
Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touch the sphere, calculated using surface to volume ratio of Hexakis Icosahedron is calculated using Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/Surface to Volume Ratio of Hexakis Icosahedron)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5)))))). To calculate Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Hexakis Icosahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Hexakis Icosahedron 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 Insphere Radius of Hexakis Icosahedron?
In this formula, Insphere Radius of Hexakis Icosahedron uses Surface to Volume Ratio of Hexakis Icosahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*Long Edge of Hexakis Icosahedron
  • Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))
  • Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))
  • Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))
  • Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(sqrt((44*Total Surface Area of Hexakis Icosahedron)/(15*(sqrt(10*(417+(107*sqrt(5))))))))
  • Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(((88*Volume of Hexakis Icosahedron)/(25*(sqrt(6*(185+(82*sqrt(5)))))))^(1/3))
  • Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))
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