Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5))))
rc = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(RA/V*(19+(10*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 Icosidodecahedron - (Measured in Meter) - Circumsphere Radius of Truncated Icosidodecahedron is the radius of the sphere that contains the Truncated Icosidodecahedron in such a way that all the vertices are lying on the sphere.
SA:V of Truncated Icosidodecahedron - (Measured in 1 per Meter) - SA:V of Truncated Icosidodecahedron is the numerical ratio of the total surface area of a Truncated Icosidodecahedron to the volume of the Truncated Icosidodecahedron.
STEP 1: Convert Input(s) to Base Unit
SA:V of Truncated Icosidodecahedron: 0.1 1 per Meter --> 0.1 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(RA/V*(19+(10*sqrt(5)))) --> sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(0.1*(19+(10*sqrt(5))))
Evaluating ... ...
rc = 32.0462362391916
STEP 3: Convert Result to Output's Unit
32.0462362391916 Meter --> No Conversion Required
FINAL ANSWER
32.0462362391916 32.04624 Meter <-- Circumsphere Radius of Truncated Icosidodecahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has created this Calculator and 2000+ more calculators!
Verified by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has verified this Calculator and 1700+ more calculators!

5 Circumsphere Radius of Truncated Icosidodecahedron Calculators

Circumsphere Radius of Truncated Icosidodecahedron given Total Surface Area
Go Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))
Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio
Go Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5))))
Circumsphere Radius of Truncated Icosidodecahedron given Midsphere Radius
Go Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*Midsphere Radius of Truncated Icosidodecahedron/sqrt(30+(12*sqrt(5)))
Circumsphere Radius of Truncated Icosidodecahedron given Volume
Go Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)
Circumsphere Radius of Truncated Icosidodecahedron
Go Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron

Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio Formula

Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5))))
rc = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(RA/V*(19+(10*sqrt(5))))

What is a Truncated Icosidodecahedron?

In geometry, the Truncated Icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal non-prismatic solids constructed by two or more types of regular polygon faces. It has 62 faces which include 30 squares, 20 regular hexagons and 12 regular decagons. Each vertex is identical in such a way that, one square, one hexagon and one decagon join at each vertex. It has the most edges and vertices of all Platonic and Archimedean solids, though the snub dodecahedron has more number of faces. Out of all vertex-transitive polyhedra, it occupies the largest percentage (89.80%) of the volume of a sphere in which it is inscribed, very narrowly beating the Snub Dodecahedron (89.63%) and Small Rhombicosidodecahedron (89.23%), and less narrowly beating the Truncated Icosahedron (86.74%).

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

Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio calculator uses Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))) to calculate the Circumsphere Radius of Truncated Icosidodecahedron, Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Truncated Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron. Circumsphere Radius of Truncated Icosidodecahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio, enter SA:V of Truncated Icosidodecahedron (RA/V) and hit the calculate button. Here is how the Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 32.04624 = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(0.1*(19+(10*sqrt(5)))).

FAQ

What is Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio?
Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Truncated Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron and is represented as rc = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(RA/V*(19+(10*sqrt(5)))) or Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))). SA:V of Truncated Icosidodecahedron is the numerical ratio of the total surface area of a Truncated Icosidodecahedron to the volume of the Truncated Icosidodecahedron.
How to calculate Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio?
Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Truncated Icosidodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the surface to volume ratio of the Truncated Icosidodecahedron is calculated using Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*(3*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))/(SA:V of Truncated Icosidodecahedron*(19+(10*sqrt(5)))). To calculate Circumsphere Radius of Truncated Icosidodecahedron given Surface to Volume Ratio, you need SA:V of Truncated Icosidodecahedron (RA/V). With our tool, you need to enter the respective value for SA:V of Truncated Icosidodecahedron 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 Icosidodecahedron?
In this formula, Circumsphere Radius of Truncated Icosidodecahedron uses SA:V of Truncated Icosidodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron
  • Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))
  • Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)
  • Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))*Midsphere Radius of Truncated Icosidodecahedron/sqrt(30+(12*sqrt(5)))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!