Circumsphere Radius of Rotunda given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Rotunda is the numerical ratio of the total surface area of a Rotunda to the volume of the Rotunda.ⓘ Surface to Volume Ratio of Rotunda [R_A/V]

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✖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.ⓘ Circumsphere Radius of Rotunda given Surface to Volume Ratio [r_c]

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Circumsphere Radius of Rotunda given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))))
r_c = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(R_A/V*1/12*(45+(17*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 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.
Surface to Volume Ratio of Rotunda - (Measured in 1 per Meter) - Surface to Volume Ratio of Rotunda is the numerical ratio of the total surface area of a Rotunda to the volume of the Rotunda.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Rotunda: 0.3 1 per Meter --> 0.3 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(R_A/V*1/12*(45+(17*sqrt(5))))) --> 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(0.3*1/12*(45+(17*sqrt(5)))))

Evaluating ... ...

r_c = 17.4230358134644

STEP 3: Convert Result to Output's Unit

17.4230358134644 Meter --> No Conversion Required

FINAL ANSWER

17.4230358134644 ≈ 17.42304 Meter <-- Circumsphere Radius of Rotunda

(Calculation completed in 00.004 seconds)

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< Circumsphere Radius of Rotunda Calculators

Circumsphere Radius of Rotunda given Total Surface Area

LaTeX 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

LaTeX Go Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*Height of Rotunda/(sqrt(1+2/sqrt(5)))

Circumsphere Radius of Rotunda given Volume

LaTeX 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

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

Circumsphere Radius of Rotunda given Surface to Volume Ratio Formula

LaTeX Go

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 given Surface to Volume Ratio?

Circumsphere Radius of Rotunda given Surface to Volume Ratio calculator uses 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))))) to calculate the Circumsphere Radius of Rotunda, The Circumsphere Radius of Rotunda given Surface to Volume Ratio 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 calculated using the surface to volume ratio of the Rotunda. Circumsphere Radius of Rotunda is denoted by r_c symbol.

How to calculate Circumsphere Radius of Rotunda given Surface to Volume Ratio using this online calculator? To use this online calculator for Circumsphere Radius of Rotunda given Surface to Volume Ratio, enter Surface to Volume Ratio of Rotunda (R_A/V) and hit the calculate button. Here is how the Circumsphere Radius of Rotunda given Surface to Volume Ratio calculation can be explained with given input values -> 17.42304 = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(0.3*1/12*(45+(17*sqrt(5))))).

FAQ

What is Circumsphere Radius of Rotunda given Surface to Volume Ratio?

The Circumsphere Radius of Rotunda given Surface to Volume Ratio 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 calculated using the surface to volume ratio of the Rotunda and is represented as r_c = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(R_A/V*1/12*(45+(17*sqrt(5))))) or 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))))). Surface to Volume Ratio of Rotunda is the numerical ratio of the total surface area of a Rotunda to the volume of the Rotunda.

How to calculate Circumsphere Radius of Rotunda given Surface to Volume Ratio?

The Circumsphere Radius of Rotunda given Surface to Volume Ratio 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 calculated using the surface to volume ratio of the Rotunda is calculated using 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))))). To calculate Circumsphere Radius of Rotunda given Surface to Volume Ratio, you need Surface to Volume Ratio of Rotunda (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio of Rotunda. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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