Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*Midsphere Radius of Truncated Dodecahedron/(5+(3*sqrt(5)))
rc = sqrt(74+(30*sqrt(5)))*rm/(5+(3*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 Dodecahedron - (Measured in Meter) - Circumsphere Radius of Truncated Dodecahedron is the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere.
Midsphere Radius of Truncated Dodecahedron - (Measured in Meter) - Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Truncated Dodecahedron: 29 Meter --> 29 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt(74+(30*sqrt(5)))*rm/(5+(3*sqrt(5))) --> sqrt(74+(30*sqrt(5)))*29/(5+(3*sqrt(5)))
Evaluating ... ...
rc = 29.4200620202746
STEP 3: Convert Result to Output's Unit
29.4200620202746 Meter --> No Conversion Required
FINAL ANSWER
29.4200620202746 29.42006 Meter <-- Circumsphere Radius of Truncated Dodecahedron
(Calculation completed in 00.020 seconds)

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6 Circumsphere Radius of Truncated Dodecahedron Calculators

Circumsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio
Go Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
Circumsphere Radius of Truncated Dodecahedron given Total Surface Area
Go Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*(sqrt(5+(2*sqrt(5))))))))
Circumsphere Radius of Truncated Dodecahedron given Volume
Go Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
Circumsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length
Go Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius
Go Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*Midsphere Radius of Truncated Dodecahedron/(5+(3*sqrt(5)))
Circumsphere Radius of Truncated Dodecahedron
Go Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron

Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius Formula

Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*Midsphere Radius of Truncated Dodecahedron/(5+(3*sqrt(5)))
rc = sqrt(74+(30*sqrt(5)))*rm/(5+(3*sqrt(5)))

What is a Truncated Dodecahedron?

In geometry, the Truncated Dodecahedron is an Archimedean solid. It has a total of 32 faces - 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Each vertex is identical in such a way that two decagonal faces and one triangular face join at each vertex. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. The Truncated Dodecahedron has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: hexagonal and pentagonal.

How to Calculate Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius?

Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius calculator uses Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*Midsphere Radius of Truncated Dodecahedron/(5+(3*sqrt(5))) to calculate the Circumsphere Radius of Truncated Dodecahedron, Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius formula is defined as the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the midsphere radius of the Truncated Dodecahedron. Circumsphere Radius of Truncated Dodecahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius, enter Midsphere Radius of Truncated Dodecahedron (rm) and hit the calculate button. Here is how the Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 29.42006 = sqrt(74+(30*sqrt(5)))*29/(5+(3*sqrt(5))).

FAQ

What is Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius?
Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius formula is defined as the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the midsphere radius of the Truncated Dodecahedron and is represented as rc = sqrt(74+(30*sqrt(5)))*rm/(5+(3*sqrt(5))) or Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*Midsphere Radius of Truncated Dodecahedron/(5+(3*sqrt(5))). Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere.
How to calculate Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius?
Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius formula is defined as the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the midsphere radius of the Truncated Dodecahedron is calculated using Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*Midsphere Radius of Truncated Dodecahedron/(5+(3*sqrt(5))). To calculate Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius, you need Midsphere Radius of Truncated Dodecahedron (rm). With our tool, you need to enter the respective value for Midsphere Radius of Truncated Dodecahedron 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 Dodecahedron?
In this formula, Circumsphere Radius of Truncated Dodecahedron uses Midsphere Radius of Truncated Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
  • Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
  • Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*(sqrt(5+(2*sqrt(5))))))))
  • Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)
  • Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5))))
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