Volume of Great Dodecahedron given Circumsphere Radius Calculator

✖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 [r_c]

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✖Volume of Great Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron.ⓘ Volume of Great Dodecahedron given Circumsphere Radius [V]

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Formula

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Volume of Great Dodecahedron given Circumsphere Radius

Formula

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

Example

`"1309.366m³"=5/4*(sqrt(5)-1)*((4*"9m")/sqrt(10+(2*sqrt(5))))^3`

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Volume of Great Dodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Great Dodecahedron: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/4*(sqrt(5)-1)*((4*r_c)/sqrt(10+(2*sqrt(5))))^3 --> 5/4*(sqrt(5)-1)*((4*9)/sqrt(10+(2*sqrt(5))))^3

Evaluating ... ...

V = 1309.36557970607

STEP 3: Convert Result to Output's Unit

1309.36557970607 Cubic Meter --> No Conversion Required

FINAL ANSWER

1309.36557970607 ≈ 1309.366 Cubic Meter <-- Volume 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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< 6 Volume of Great Dodecahedron Calculators

Volume of Great Dodecahedron given Surface to Volume Ratio

Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron))^3

Volume of Great Dodecahedron given Total Surface Area

Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))^(3/2)

Volume of Great Dodecahedron given Circumsphere Radius

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

Volume of Great Dodecahedron given Pyramidal Height

Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^3

Volume of Great Dodecahedron given Ridge Length

Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^3

Volume of Great Dodecahedron

Go Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron^3

Volume of Great Dodecahedron given Circumsphere Radius Formula

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

Volume of Great Dodecahedron given Circumsphere Radius calculator uses Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3 to calculate the Volume of Great Dodecahedron, Volume of Great Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron, calculated using its circumsphere radius. Volume of Great Dodecahedron is denoted by V symbol.

How to calculate Volume of Great Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Volume of Great Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Great Dodecahedron (r_c) and hit the calculate button. Here is how the Volume of Great Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 1309.366 = 5/4*(sqrt(5)-1)*((4*9)/sqrt(10+(2*sqrt(5))))^3.

FAQ

What is Volume of Great Dodecahedron given Circumsphere Radius?

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

How to calculate Volume of Great Dodecahedron given Circumsphere Radius?

Volume of Great Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron, calculated using its circumsphere radius is calculated using Volume of Great Dodecahedron = 5/4*(sqrt(5)-1)*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^3. To calculate Volume of Great Dodecahedron given Circumsphere Radius, you need Circumsphere Radius of Great Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Volume of Great Dodecahedron?

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

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

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