Circumsphere Radius of Truncated Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
rc = sqrt(74+(30*sqrt(5)))/4*le
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.
Edge Length of Truncated Dodecahedron - (Measured in Meter) - Edge Length of Truncated Dodecahedron is the length of any edge of the Truncated Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Truncated Dodecahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt(74+(30*sqrt(5)))/4*le --> sqrt(74+(30*sqrt(5)))/4*10
Evaluating ... ...
rc = 29.694490158634
STEP 3: Convert Result to Output's Unit
29.694490158634 Meter --> No Conversion Required
FINAL ANSWER
29.694490158634 29.69449 Meter <-- Circumsphere Radius of Truncated Dodecahedron
(Calculation completed in 00.004 seconds)

Credits

Creator Image
Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has created this Calculator and 2000+ more calculators!
Verifier Image
Verified by Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has verified this Calculator and 1100+ more calculators!

Circumsphere Radius of Truncated Dodecahedron Calculators

Circumsphere Radius of Truncated Dodecahedron given Total Surface Area
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ Go Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron

Circumsphere Radius of Truncated Dodecahedron Formula

​LaTeX ​Go
Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
rc = sqrt(74+(30*sqrt(5)))/4*le

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?

Circumsphere Radius of Truncated Dodecahedron calculator uses Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron to calculate the Circumsphere Radius of Truncated Dodecahedron, Circumsphere Radius of Truncated Dodecahedron 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. Circumsphere Radius of Truncated Dodecahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Truncated Dodecahedron using this online calculator? To use this online calculator for Circumsphere Radius of Truncated Dodecahedron, enter Edge Length of Truncated Dodecahedron (le) and hit the calculate button. Here is how the Circumsphere Radius of Truncated Dodecahedron calculation can be explained with given input values -> 29.69449 = sqrt(74+(30*sqrt(5)))/4*10.

FAQ

What is Circumsphere Radius of Truncated Dodecahedron?
Circumsphere Radius of Truncated Dodecahedron 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 is represented as rc = sqrt(74+(30*sqrt(5)))/4*le or Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron. Edge Length of Truncated Dodecahedron is the length of any edge of the Truncated Dodecahedron.
How to calculate Circumsphere Radius of Truncated Dodecahedron?
Circumsphere Radius of Truncated Dodecahedron 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 is calculated using Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron. To calculate Circumsphere Radius of Truncated Dodecahedron, you need Edge Length of Truncated Dodecahedron (le). With our tool, you need to enter the respective value for Edge Length 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 Edge Length of Truncated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!