Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area Calculator

✖Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.ⓘ Total Surface Area of Great Stellated Dodecahedron [TSA]

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✖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.ⓘ Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area [r_c]

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Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5)))))
r_c = (sqrt(3)*(3+sqrt(5)))/4*sqrt(TSA/(15*sqrt(5+(2*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

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.
Total Surface Area of Great Stellated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Great Stellated Dodecahedron: 4600 Square Meter --> 4600 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (sqrt(3)*(3+sqrt(5)))/4*sqrt(TSA/(15*sqrt(5+(2*sqrt(5))))) --> (sqrt(3)*(3+sqrt(5)))/4*sqrt(4600/(15*sqrt(5+(2*sqrt(5)))))

Evaluating ... ...

r_c = 22.6322232144644

STEP 3: Convert Result to Output's Unit

22.6322232144644 Meter --> No Conversion Required

FINAL ANSWER

22.6322232144644 ≈ 22.63222 Meter <-- Circumradius of Great Stellated Dodecahedron

(Calculation completed in 00.006 seconds)

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< Radius of Great Stellated Dodecahedron Calculators

Circumsphere Radius of Great Stellated Dodecahedron given Ridge Length

LaTeX Go Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/2*(1*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))

Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord

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

Circumsphere Radius of Great Stellated Dodecahedron

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

Circumsphere Radius of Great Stellated Dodecahedron given Pyramidal Height

LaTeX Go Circumradius of Great Stellated Dodecahedron = (3*Pyramidal Height of Great Stellated Dodecahedron)/2

Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area Formula

LaTeX Go

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 Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area?

Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area calculator uses Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5))))) to calculate the Circumradius of Great Stellated Dodecahedron, Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its total surface area. Circumradius of Great Stellated Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area, enter Total Surface Area of Great Stellated Dodecahedron (TSA) and hit the calculate button. Here is how the Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area calculation can be explained with given input values -> 22.63222 = (sqrt(3)*(3+sqrt(5)))/4*sqrt(4600/(15*sqrt(5+(2*sqrt(5))))).

FAQ

What is Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area?

Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its total surface area and is represented as r_c = (sqrt(3)*(3+sqrt(5)))/4*sqrt(TSA/(15*sqrt(5+(2*sqrt(5))))) or Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5))))). Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.

How to calculate Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area?

Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its total surface area is calculated using Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5))))). To calculate Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area, you need Total Surface Area of Great Stellated Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Circumradius of Great Stellated Dodecahedron?

In this formula, Circumradius of Great Stellated Dodecahedron uses Total Surface Area of Great Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Edge Length of Great Stellated Dodecahedron
Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/2*(1*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))

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