Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio Calculator

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

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✖Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.ⓘ Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio [r_c]

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Formula

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Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio

Formula

`"r"_{"c"} = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"R"_{"A/V"})`

Example

`"9.583148m"=sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"0.7m⁻¹")`

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Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)
r_c = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V)
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 Great Dodecahedron - (Measured in Meter) - Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.
Surface to Volume Ratio of Great Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Great Dodecahedron: 0.7 1 per Meter --> 0.7 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V) --> sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7)

Evaluating ... ...

r_c = 9.5831484749991

STEP 3: Convert Result to Output's Unit

9.5831484749991 Meter --> No Conversion Required

FINAL ANSWER

9.5831484749991 ≈ 9.583148 Meter <-- Circumsphere Radius of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 6 Circumsphere Radius of Great Dodecahedron Calculators

Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio

Go Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)

Circumsphere Radius of Great Dodecahedron given Total Surface Area

Go Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

Circumsphere Radius of Great Dodecahedron given Pyramidal Height

Go Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))

Circumsphere Radius of Great Dodecahedron given Volume

Go Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3)

Circumsphere Radius of Great Dodecahedron given Ridge Length

Go Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)

Circumsphere Radius of Great Dodecahedron

Go Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Great Dodecahedron

Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio Formula

What is Great Dodecahedron?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio?

Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio calculator uses Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron) to calculate the Circumsphere Radius of Great Dodecahedron, Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere, calculated using its surface to volume ratio. Circumsphere Radius of Great Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Great Dodecahedron (R_A/V) and hit the calculate button. Here is how the Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 9.583148 = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7).

FAQ

What is Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio?

Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere, calculated using its surface to volume ratio and is represented as r_c = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V) or Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron). Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.

How to calculate Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio?

Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere, calculated using its surface to volume ratio is calculated using Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron). To calculate Circumsphere Radius of Great Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Great Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Great 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 Great Dodecahedron?

In this formula, Circumsphere Radius of Great Dodecahedron uses Surface to Volume Ratio of Great Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Great Dodecahedron
Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)
Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))
Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))
Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3)

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