Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))
rm = sqrt(30+(12*sqrt(5)))/2*sqrt(TSA/(30*(1+sqrt(3)+sqrt(5+(2*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
Midsphere Radius of Truncated Icosidodecahedron - (Measured in Meter) - Midsphere Radius of Truncated Icosidodecahedron is the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere.
Total Surface Area of Truncated Icosidodecahedron - (Measured in Square Meter) - Total Surface Area of Truncated Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Truncated Icosidodecahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Truncated Icosidodecahedron: 17000 Square Meter --> 17000 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(30+(12*sqrt(5)))/2*sqrt(TSA/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))) --> sqrt(30+(12*sqrt(5)))/2*sqrt(17000/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))
Evaluating ... ...
rm = 37.2267640920716
STEP 3: Convert Result to Output's Unit
37.2267640920716 Meter --> No Conversion Required
FINAL ANSWER
37.2267640920716 37.22676 Meter <-- Midsphere Radius of Truncated Icosidodecahedron
(Calculation completed in 00.004 seconds)

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Midsphere Radius of Truncated Icosidodecahedron Calculators

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

Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area Formula

​LaTeX ​Go
Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))))
rm = sqrt(30+(12*sqrt(5)))/2*sqrt(TSA/(30*(1+sqrt(3)+sqrt(5+(2*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 Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area?

Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area calculator uses Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))) to calculate the Midsphere Radius of Truncated Icosidodecahedron, Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Truncated Icosidodecahedron. Midsphere Radius of Truncated Icosidodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area using this online calculator? To use this online calculator for Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area, enter Total Surface Area of Truncated Icosidodecahedron (TSA) and hit the calculate button. Here is how the Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area calculation can be explained with given input values -> 37.22676 = sqrt(30+(12*sqrt(5)))/2*sqrt(17000/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))).

FAQ

What is Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area?
Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Truncated Icosidodecahedron and is represented as rm = sqrt(30+(12*sqrt(5)))/2*sqrt(TSA/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))) or Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))). Total Surface Area of Truncated Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Truncated Icosidodecahedron.
How to calculate Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area?
Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Truncated Icosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Truncated Icosidodecahedron is calculated using Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*sqrt(Total Surface Area of Truncated Icosidodecahedron/(30*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))))). To calculate Midsphere Radius of Truncated Icosidodecahedron given Total Surface Area, you need Total Surface Area of Truncated Icosidodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Midsphere Radius of Truncated Icosidodecahedron?
In this formula, Midsphere Radius of Truncated Icosidodecahedron uses Total Surface Area of Truncated Icosidodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*Edge Length of Truncated Icosidodecahedron
  • Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)
  • Midsphere Radius of Truncated Icosidodecahedron = sqrt(30+(12*sqrt(5)))*Circumsphere Radius of Truncated Icosidodecahedron/sqrt(31+(12*sqrt(5)))
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