Circumsphere Radius of Rotunda Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Edge Length of Rotunda
rc = 1/2*(1+sqrt(5))*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 Rotunda - (Measured in Meter) - Circumsphere Radius of Rotunda is the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere.
Edge Length of Rotunda - (Measured in Meter) - Edge Length of Rotunda is the length of any edge of the Rotunda.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Rotunda: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = 1/2*(1+sqrt(5))*le --> 1/2*(1+sqrt(5))*10
Evaluating ... ...
rc = 16.1803398874989
STEP 3: Convert Result to Output's Unit
16.1803398874989 Meter --> No Conversion Required
FINAL ANSWER
16.1803398874989 16.18034 Meter <-- Circumsphere Radius of Rotunda
(Calculation completed in 00.004 seconds)

Credits

Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has created this Calculator and 2000+ more calculators!
Verified by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has verified this Calculator and 1700+ more calculators!

5 Circumsphere Radius of Rotunda Calculators

Circumsphere Radius of Rotunda given Surface to Volume Ratio
Go Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(Surface to Volume Ratio of Rotunda*1/12*(45+(17*sqrt(5)))))
Circumsphere Radius of Rotunda given Total Surface Area
Go Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))
Circumsphere Radius of Rotunda given Height
Go Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Height of Rotunda/(sqrt(1+2/sqrt(5)))
Circumsphere Radius of Rotunda given Volume
Go Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*(Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(1/3)
Circumsphere Radius of Rotunda
Go Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Edge Length of Rotunda

Circumsphere Radius of Rotunda Formula

Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Edge Length of Rotunda
rc = 1/2*(1+sqrt(5))*le

What is a Rotunda?

A Rotunda is similar to a cupola but has pentagons instead of quadrangles as side faces. The regular pentagonal rotunda is Johnson solid which is generally denoted by J6. It has 17 faces which include a regular pentagonal face at the top, a regular decagonal face at the bottom, 10 equilateral triangular faces, and 5 regular pentagonal faces. Also, It has 35 edges and 20 vertices.

How to Calculate Circumsphere Radius of Rotunda?

Circumsphere Radius of Rotunda calculator uses Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Edge Length of Rotunda to calculate the Circumsphere Radius of Rotunda, The Circumsphere Radius of Rotunda formula is defined as the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere. Circumsphere Radius of Rotunda is denoted by rc symbol.

How to calculate Circumsphere Radius of Rotunda using this online calculator? To use this online calculator for Circumsphere Radius of Rotunda, enter Edge Length of Rotunda (le) and hit the calculate button. Here is how the Circumsphere Radius of Rotunda calculation can be explained with given input values -> 16.18034 = 1/2*(1+sqrt(5))*10.

FAQ

What is Circumsphere Radius of Rotunda?
The Circumsphere Radius of Rotunda formula is defined as the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere and is represented as rc = 1/2*(1+sqrt(5))*le or Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Edge Length of Rotunda. Edge Length of Rotunda is the length of any edge of the Rotunda.
How to calculate Circumsphere Radius of Rotunda?
The Circumsphere Radius of Rotunda formula is defined as the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere is calculated using Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Edge Length of Rotunda. To calculate Circumsphere Radius of Rotunda, you need Edge Length of Rotunda (le). With our tool, you need to enter the respective value for Edge Length of Rotunda 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 Rotunda?
In this formula, Circumsphere Radius of Rotunda uses Edge Length of Rotunda. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Height of Rotunda/(sqrt(1+2/sqrt(5)))
  • Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))
  • Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*(Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(1/3)
  • Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(Surface to Volume Ratio of Rotunda*1/12*(45+(17*sqrt(5)))))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!