Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Truncated Icosidodecahedron = 30*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))
TSA = 30*((2*rm)/(sqrt(30+(12*sqrt(5)))))^2*(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
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.
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.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Truncated Icosidodecahedron: 37 Meter --> 37 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = 30*((2*rm)/(sqrt(30+(12*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))) --> 30*((2*37)/(sqrt(30+(12*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5))))
Evaluating ... ...
TSA = 16793.5222968515
STEP 3: Convert Result to Output's Unit
16793.5222968515 Square Meter --> No Conversion Required
FINAL ANSWER
16793.5222968515 16793.52 Square Meter <-- Total Surface Area of Truncated Icosidodecahedron
(Calculation completed in 00.004 seconds)

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Total Surface Area of Truncated Icosidodecahedron Calculators

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

Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius Formula

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

Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius calculator uses Total Surface Area of Truncated Icosidodecahedron = 30*((2*Midsphere Radius of Truncated Icosidodecahedron)/(sqrt(30+(12*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))) to calculate the Total Surface Area of Truncated Icosidodecahedron, Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosidodecahedron, and calculated using the midsphere radius of the Truncated Icosidodecahedron. Total Surface Area of Truncated Icosidodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius, enter Midsphere Radius of Truncated Icosidodecahedron (rm) and hit the calculate button. Here is how the Total Surface Area of Truncated Icosidodecahedron given Midsphere Radius calculation can be explained with given input values -> 16793.52 = 30*((2*37)/(sqrt(30+(12*sqrt(5)))))^2*(1+sqrt(3)+sqrt(5+(2*sqrt(5)))).

FAQ

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