Circumsphere Radius of Great Dodecahedron given Volume Calculator

✖Volume of Great Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron.ⓘ Volume of Great Dodecahedron [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 Volume [r_c]

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Formula

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Circumsphere Radius of Great Dodecahedron given Volume

Formula

`"r"_{"c"} = sqrt(10+(2*sqrt(5)))/4*((4*"V")/(5*(sqrt(5)-1)))^(1/3)`

Example

`"9.520639m"=sqrt(10+(2*sqrt(5)))/4*((4*"1550m³")/(5*(sqrt(5)-1)))^(1/3)`

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Circumsphere Radius of Great Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3)
r_c = sqrt(10+(2*sqrt(5)))/4*((4*V)/(5*(sqrt(5)-1)))^(1/3)
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.
Volume of Great Dodecahedron - (Measured in Cubic Meter) - Volume of Great Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Great Dodecahedron: 1550 Cubic Meter --> 1550 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(10+(2*sqrt(5)))/4*((4*V)/(5*(sqrt(5)-1)))^(1/3) --> sqrt(10+(2*sqrt(5)))/4*((4*1550)/(5*(sqrt(5)-1)))^(1/3)

Evaluating ... ...

r_c = 9.52063908928949

STEP 3: Convert Result to Output's Unit

9.52063908928949 Meter --> No Conversion Required

FINAL ANSWER

9.52063908928949 ≈ 9.520639 Meter <-- Circumsphere Radius of Great Dodecahedron

(Calculation completed in 00.006 seconds)

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Home » Math » Geometry » 3D Geometry » Great Dodecahedron » Radius of Great Dodecahedron » Circumsphere Radius of Great Dodecahedron » Circumsphere Radius of Great Dodecahedron given Volume

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

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 Volume Formula

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

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 Volume?

Circumsphere Radius of Great Dodecahedron given Volume calculator uses Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3) to calculate the Circumsphere Radius of Great Dodecahedron, Circumsphere Radius of Great Dodecahedron given Volume 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 volume. Circumsphere Radius of Great Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Dodecahedron given Volume using this online calculator? To use this online calculator for Circumsphere Radius of Great Dodecahedron given Volume, enter Volume of Great Dodecahedron (V) and hit the calculate button. Here is how the Circumsphere Radius of Great Dodecahedron given Volume calculation can be explained with given input values -> 9.520639 = sqrt(10+(2*sqrt(5)))/4*((4*1550)/(5*(sqrt(5)-1)))^(1/3).

FAQ

What is Circumsphere Radius of Great Dodecahedron given Volume?

Circumsphere Radius of Great Dodecahedron given Volume 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 volume and is represented as r_c = sqrt(10+(2*sqrt(5)))/4*((4*V)/(5*(sqrt(5)-1)))^(1/3) or Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3). Volume of Great Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron.

How to calculate Circumsphere Radius of Great Dodecahedron given Volume?

Circumsphere Radius of Great Dodecahedron given Volume 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 volume is calculated using Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3). To calculate Circumsphere Radius of Great Dodecahedron given Volume, you need Volume of Great Dodecahedron (V). With our tool, you need to enter the respective value for Volume 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 Volume 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*(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)

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