Surface to Volume Ratio of Rotunda given Circumsphere Radius Calculator

✖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 [r_c]

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✖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 given Circumsphere Radius [R_A/V]

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Surface to Volume Ratio of Rotunda given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Rotunda = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((2*Circumsphere Radius of Rotunda)/(1+sqrt(5))*1/12*(45+(17*sqrt(5))))
R_A/V = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((2*r_c)/(1+sqrt(5))*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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Rotunda: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((2*r_c)/(1+sqrt(5))*1/12*(45+(17*sqrt(5)))) --> (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((2*16)/(1+sqrt(5))*1/12*(45+(17*sqrt(5))))

Evaluating ... ...

R_A/V = 0.326681921502458

STEP 3: Convert Result to Output's Unit

0.326681921502458 1 per Meter --> No Conversion Required

FINAL ANSWER

0.326681921502458 ≈ 0.326682 1 per Meter <-- Surface to Volume Ratio of Rotunda

(Calculation completed in 00.004 seconds)

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< Surface to Volume Ratio of Rotunda Calculators

Surface to Volume Ratio of Rotunda given Total Surface Area

LaTeX Go Surface to Volume Ratio of Rotunda = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))*1/12*(45+(17*sqrt(5))))

Surface to Volume Ratio of Rotunda given Height

LaTeX Go Surface to Volume Ratio of Rotunda = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(Height of Rotunda/(sqrt(1+2/sqrt(5)))*1/12*(45+(17*sqrt(5))))

Surface to Volume Ratio of Rotunda given Volume

LaTeX Go Surface to Volume Ratio of Rotunda = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(1/3)*1/12*(45+(17*sqrt(5))))

Surface to Volume Ratio of Rotunda

LaTeX Go Surface to Volume Ratio of Rotunda = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(Edge Length of Rotunda*1/12*(45+(17*sqrt(5))))

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

Surface to Volume Ratio of Rotunda given Circumsphere Radius calculator uses Surface to Volume Ratio of Rotunda = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((2*Circumsphere Radius of Rotunda)/(1+sqrt(5))*1/12*(45+(17*sqrt(5)))) to calculate the Surface to Volume Ratio of Rotunda, The Surface to Volume Ratio of Rotunda given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Rotunda to the volume of the Rotunda and is calculated using the circumsphere radius of the Rotunda. Surface to Volume Ratio of Rotunda is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Rotunda given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Rotunda given Circumsphere Radius, enter Circumsphere Radius of Rotunda (r_c) and hit the calculate button. Here is how the Surface to Volume Ratio of Rotunda given Circumsphere Radius calculation can be explained with given input values -> 0.326682 = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((2*16)/(1+sqrt(5))*1/12*(45+(17*sqrt(5)))).

FAQ

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

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

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

The Surface to Volume Ratio of Rotunda given Circumsphere Radius formula is defined as the numerical ratio of the total surface area of a Rotunda to the volume of the Rotunda and is calculated using the circumsphere radius of the Rotunda is calculated using Surface to Volume Ratio of Rotunda = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/((2*Circumsphere Radius of Rotunda)/(1+sqrt(5))*1/12*(45+(17*sqrt(5)))). To calculate Surface to Volume Ratio of Rotunda given Circumsphere Radius, you need Circumsphere Radius of Rotunda (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Surface to Volume Ratio of Rotunda?

In this formula, Surface to Volume Ratio of Rotunda uses Circumsphere Radius of Rotunda. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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