Volume of Great Stellated Dodecahedron given Circumradius Calculator

✖Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.ⓘ Circumradius of Great Stellated Dodecahedron [r_c]

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

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Formula

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Volume of Great Stellated Dodecahedron given Circumradius

Formula

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

Example

`"6832.522m³"=5/4*(3+sqrt(5))*((4*"23m")/(sqrt(3)*(3+sqrt(5))))^3`

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Volume of Great Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3
V = 5/4*(3+sqrt(5))*((4*r_c)/(sqrt(3)*(3+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 Stellated Dodecahedron - (Measured in Cubic Meter) - Volume of Great Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron.
Circumradius of Great Stellated Dodecahedron - (Measured in Meter) - Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Great Stellated Dodecahedron: 23 Meter --> 23 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/4*(3+sqrt(5))*((4*r_c)/(sqrt(3)*(3+sqrt(5))))^3 --> 5/4*(3+sqrt(5))*((4*23)/(sqrt(3)*(3+sqrt(5))))^3

Evaluating ... ...

V = 6832.52234435199

STEP 3: Convert Result to Output's Unit

6832.52234435199 Cubic Meter --> No Conversion Required

FINAL ANSWER

6832.52234435199 ≈ 6832.522 Cubic Meter <-- Volume of Great Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Great Stellated Dodecahedron » Volume of Great Stellated Dodecahedron » Volume of Great Stellated Dodecahedron given Circumradius

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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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< 7 Volume of Great Stellated Dodecahedron Calculators

Volume of Great Stellated Dodecahedron given Surface to Volume Ratio

Go Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^3

Volume of Great Stellated Dodecahedron given Total Surface Area

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

Volume of Great Stellated Dodecahedron given Pyramidal Height

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

Volume of Great Stellated Dodecahedron given Circumradius

Go Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Great Stellated Dodecahedron given Ridge Length

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

Volume of Great Stellated Dodecahedron given Pentagram Chord

Go Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^3

Volume of Great Stellated Dodecahedron

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

Volume of Great Stellated Dodecahedron given Circumradius Formula

Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3
V = 5/4*(3+sqrt(5))*((4*r_c)/(sqrt(3)*(3+sqrt(5))))^3

What is Great Stellated Dodecahedron?

The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

How to Calculate Volume of Great Stellated Dodecahedron given Circumradius?

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

How to calculate Volume of Great Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Volume of Great Stellated Dodecahedron given Circumradius, enter Circumradius of Great Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Volume of Great Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 6832.522 = 5/4*(3+sqrt(5))*((4*23)/(sqrt(3)*(3+sqrt(5))))^3.

FAQ

What is Volume of Great Stellated Dodecahedron given Circumradius?

Volume of Great Stellated Dodecahedron given Circumradius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Great Stellated Dodecahedron, calculated using its circumradius and is represented as V = 5/4*(3+sqrt(5))*((4*r_c)/(sqrt(3)*(3+sqrt(5))))^3 or Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3. Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

How to calculate Volume of Great Stellated Dodecahedron given Circumradius?

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

In this formula, Volume of Great Stellated Dodecahedron uses Circumradius of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*Edge Length of Great Stellated Dodecahedron^3
Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^3
Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^3
Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^3
Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))^(3/2)
Volume of Great Stellated Dodecahedron = 5/4*(3+sqrt(5))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^3

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