Circumsphere Radius of Truncated Icosidodecahedron given Volume Calculator

✖Volume of Truncated Icosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron.ⓘ Volume of Truncated Icosidodecahedron [V]

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✖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.ⓘ Circumsphere Radius of Truncated Icosidodecahedron given Volume [r_c]

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Formula

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Circumsphere Radius of Truncated Icosidodecahedron given Volume

Formula

`"r"_{"c"} = sqrt(31+(12*sqrt(5)))/2*("V"/(5*(19+(10*sqrt(5)))))^(1/3)`

Example

`"38.21886m"=sqrt(31+(12*sqrt(5)))/2*("210000m³"/(5*(19+(10*sqrt(5)))))^(1/3)`

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Circumsphere Radius of Truncated Icosidodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3)
r_c = sqrt(31+(12*sqrt(5)))/2*(V/(5*(19+(10*sqrt(5)))))^(1/3)
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.
Volume of Truncated Icosidodecahedron - (Measured in Cubic Meter) - Volume of Truncated Icosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Truncated Icosidodecahedron: 210000 Cubic Meter --> 210000 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(31+(12*sqrt(5)))/2*(V/(5*(19+(10*sqrt(5)))))^(1/3) --> sqrt(31+(12*sqrt(5)))/2*(210000/(5*(19+(10*sqrt(5)))))^(1/3)

Evaluating ... ...

r_c = 38.2188586998882

STEP 3: Convert Result to Output's Unit

38.2188586998882 Meter --> No Conversion Required

FINAL ANSWER

38.2188586998882 ≈ 38.21886 Meter <-- Circumsphere Radius of Truncated Icosidodecahedron

(Calculation completed in 00.020 seconds)

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< 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 Volume Formula

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 Volume?

Circumsphere Radius of Truncated Icosidodecahedron given Volume calculator uses Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3) to calculate the Circumsphere Radius of Truncated Icosidodecahedron, Circumsphere Radius of Truncated Icosidodecahedron given Volume 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 volume of the Truncated Icosidodecahedron. Circumsphere Radius of Truncated Icosidodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Truncated Icosidodecahedron given Volume using this online calculator? To use this online calculator for Circumsphere Radius of Truncated Icosidodecahedron given Volume, enter Volume of Truncated Icosidodecahedron (V) and hit the calculate button. Here is how the Circumsphere Radius of Truncated Icosidodecahedron given Volume calculation can be explained with given input values -> 38.21886 = sqrt(31+(12*sqrt(5)))/2*(210000/(5*(19+(10*sqrt(5)))))^(1/3).

FAQ

What is Circumsphere Radius of Truncated Icosidodecahedron given Volume?

Circumsphere Radius of Truncated Icosidodecahedron given Volume 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 volume of the Truncated Icosidodecahedron and is represented as r_c = sqrt(31+(12*sqrt(5)))/2*(V/(5*(19+(10*sqrt(5)))))^(1/3) or Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3). Volume of Truncated Icosidodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosidodecahedron.

How to calculate Circumsphere Radius of Truncated Icosidodecahedron given Volume?

Circumsphere Radius of Truncated Icosidodecahedron given Volume 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 volume of the Truncated Icosidodecahedron is calculated using Circumsphere Radius of Truncated Icosidodecahedron = sqrt(31+(12*sqrt(5)))/2*(Volume of Truncated Icosidodecahedron/(5*(19+(10*sqrt(5)))))^(1/3). To calculate Circumsphere Radius of Truncated Icosidodecahedron given Volume, you need Volume of Truncated Icosidodecahedron (V). With our tool, you need to enter the respective value for Volume 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 Volume 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)))*Midsphere Radius of Truncated Icosidodecahedron/sqrt(30+(12*sqrt(5)))
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))))

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