Edge Length 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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✖Edge Length of Rotunda is the length of any edge of the Rotunda.ⓘ Edge Length of Rotunda given Surface to Volume Ratio [l_e]

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Edge Length of Rotunda given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Edge Length of Rotunda - (Measured in Meter) - Edge Length of Rotunda is the length of any edge of the Rotunda.
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

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

Evaluating ... ...

l_e = 10.7680283199277

STEP 3: Convert Result to Output's Unit

10.7680283199277 Meter --> No Conversion Required

FINAL ANSWER

10.7680283199277 ≈ 10.76803 Meter <-- Edge Length of Rotunda

(Calculation completed in 00.020 seconds)

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< Edge Length of Rotunda Calculators

Edge Length of Rotunda given Total Surface Area

LaTeX Go Edge Length of Rotunda = sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))

Edge Length of Rotunda given Height

LaTeX Go Edge Length of Rotunda = Height of Rotunda/(sqrt(1+2/sqrt(5)))

Edge Length of Rotunda given Volume

LaTeX Go Edge Length of Rotunda = (Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(1/3)

Edge Length of Rotunda given Circumsphere Radius

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

Edge Length 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 Edge Length of Rotunda given Surface to Volume Ratio?

Edge Length of Rotunda given Surface to Volume Ratio calculator uses Edge Length of Rotunda = (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 Edge Length of Rotunda, The Edge Length of Rotunda given Surface to Volume Ratio formula is defined as the length of any edge of the Rotunda and is calculated using the surface to volume ratio of the Rotunda. Edge Length of Rotunda is denoted by l_e symbol.

How to calculate Edge Length of Rotunda given Surface to Volume Ratio using this online calculator? To use this online calculator for Edge Length 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 Edge Length of Rotunda given Surface to Volume Ratio calculation can be explained with given input values -> 10.76803 = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(0.3*1/12*(45+(17*sqrt(5)))).

FAQ

What is Edge Length of Rotunda given Surface to Volume Ratio?

The Edge Length of Rotunda given Surface to Volume Ratio formula is defined as the length of any edge of the Rotunda and is calculated using the surface to volume ratio of the Rotunda and is represented as l_e = (1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(R_A/V*1/12*(45+(17*sqrt(5)))) or Edge Length of Rotunda = (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 Edge Length of Rotunda given Surface to Volume Ratio?

The Edge Length of Rotunda given Surface to Volume Ratio formula is defined as the length of any edge of the Rotunda and is calculated using the surface to volume ratio of the Rotunda is calculated using Edge Length of Rotunda = (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 Edge Length 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 Edge Length of Rotunda?

In this formula, Edge Length 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 -

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

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