Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5))))
rc = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(RA/V*(125+(43*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
Circumsphere Radius of Truncated Icosahedron - (Measured in Meter) - Circumsphere Radius of Truncated Icosahedron is the radius of the sphere that contains the Truncated Icosahedron in such a way that all the vertices are lying on the sphere.
Surface to Volume Ratio of Truncated Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Truncated Icosahedron is the numerical ratio of the total surface area of a Truncated Icosahedron to the volume of the Truncated Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Truncated Icosahedron: 0.1 1 per Meter --> 0.1 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(RA/V*(125+(43*sqrt(5)))) --> sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(0.1*(125+(43*sqrt(5))))
Evaluating ... ...
rc = 32.5428671669245
STEP 3: Convert Result to Output's Unit
32.5428671669245 Meter --> No Conversion Required
FINAL ANSWER
32.5428671669245 32.54287 Meter <-- Circumsphere Radius of Truncated Icosahedron
(Calculation completed in 00.020 seconds)

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6 Circumsphere Radius of Truncated Icosahedron Calculators

Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio
Go Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5))))
Circumsphere Radius of Truncated Icosahedron given Total Surface Area
Go Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))))
Circumsphere Radius of Truncated Icosahedron given Volume
Go Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)
Circumsphere Radius of Truncated Icosahedron given Midsphere Radius
Go Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*Midsphere Radius of Truncated Icosahedron/(3*(1+sqrt(5)))
Circumsphere Radius of Truncated Icosahedron given Icosahedral Edge Length
Go Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/12*Icosahedral Edge Length of Truncated Icosahedron
Circumsphere Radius of Truncated Icosahedron
Go Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*Edge Length of Truncated Icosahedron

Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio Formula

Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5))))
rc = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(RA/V*(125+(43*sqrt(5))))

What is Truncated Icosahedron and its applications?

In geometry, the Truncated Icosahedron is an Archimedean solid, one of 13 convex isogonal non-prismatic solids whose faces are two or more types of regular polygons. It has a total of 32 faces which include 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces. This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule. It is used in the cell-transitive hyperbolic space-filling tessellation, the bi-truncated order-5 dodecahedral honeycomb.

How to Calculate Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio?

Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio calculator uses Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))) to calculate the Circumsphere Radius of Truncated Icosahedron, Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Truncated Icosahedron in such a way that all the vertices are lying on the sphere, and calculated using the surface to volume ratio of the Truncated Icosahedron. Circumsphere Radius of Truncated Icosahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Truncated Icosahedron (RA/V) and hit the calculate button. Here is how the Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 32.54287 = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(0.1*(125+(43*sqrt(5)))).

FAQ

What is Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio?
Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Truncated Icosahedron in such a way that all the vertices are lying on the sphere, and calculated using the surface to volume ratio of the Truncated Icosahedron and is represented as rc = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(RA/V*(125+(43*sqrt(5)))) or Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))). Surface to Volume Ratio of Truncated Icosahedron is the numerical ratio of the total surface area of a Truncated Icosahedron to the volume of the Truncated Icosahedron.
How to calculate Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio?
Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Truncated Icosahedron in such a way that all the vertices are lying on the sphere, and calculated using the surface to volume ratio of the Truncated Icosahedron is calculated using Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))). To calculate Circumsphere Radius of Truncated Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Truncated Icosahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Truncated 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 Circumsphere Radius of Truncated Icosahedron?
In this formula, Circumsphere Radius of Truncated Icosahedron uses Surface to Volume Ratio of Truncated Icosahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*Edge Length of Truncated Icosahedron
  • Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/12*Icosahedral Edge Length of Truncated Icosahedron
  • Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))))
  • Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)
  • Circumsphere Radius of Truncated Icosahedron = sqrt(58+(18*sqrt(5)))*Midsphere Radius of Truncated Icosahedron/(3*(1+sqrt(5)))
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