Circumsphere Radius of Great Dodecahedron given Total Surface Area Calculator

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

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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 Total Surface Area [r_c]

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Circumsphere Radius of Great Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Great Dodecahedron: 1100 Square Meter --> 1100 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(10+(2*sqrt(5)))/4*sqrt(TSA/(15*sqrt(5-(2*sqrt(5))))) --> sqrt(10+(2*sqrt(5)))/4*sqrt(1100/(15*sqrt(5-(2*sqrt(5)))))

Evaluating ... ...

r_c = 9.55490818614716

STEP 3: Convert Result to Output's Unit

9.55490818614716 Meter --> No Conversion Required

FINAL ANSWER

9.55490818614716 ≈ 9.554908 Meter <-- Circumsphere Radius of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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< Circumsphere Radius of Great Dodecahedron Calculators

Circumsphere Radius of Great Dodecahedron given Total Surface Area

LaTeX 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

LaTeX 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 Ridge Length

LaTeX 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

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

Circumsphere Radius of Great Dodecahedron given Total Surface Area Formula

LaTeX Go

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 Total Surface Area?

Circumsphere Radius of Great Dodecahedron given Total Surface Area calculator uses Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5))))) to calculate the Circumsphere Radius of Great Dodecahedron, Circumsphere Radius of Great Dodecahedron given Total Surface Area 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 total surface area. Circumsphere Radius of Great Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Circumsphere Radius of Great Dodecahedron given Total Surface Area, enter Total Surface Area of Great Dodecahedron (TSA) and hit the calculate button. Here is how the Circumsphere Radius of Great Dodecahedron given Total Surface Area calculation can be explained with given input values -> 9.554908 = sqrt(10+(2*sqrt(5)))/4*sqrt(1100/(15*sqrt(5-(2*sqrt(5))))).

FAQ

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

Circumsphere Radius of Great Dodecahedron given Total Surface Area 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 total surface area and is represented as r_c = sqrt(10+(2*sqrt(5)))/4*sqrt(TSA/(15*sqrt(5-(2*sqrt(5))))) or Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5))))). Total Surface Area of Great Dodecahedron is the total quantity of plane enclosed on the entire surface of the Great Dodecahedron.

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

Circumsphere Radius of Great Dodecahedron given Total Surface Area 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 total surface area is calculated using Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5))))). To calculate Circumsphere Radius of Great Dodecahedron given Total Surface Area, you need Total Surface Area of Great Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Total Surface Area of Great Dodecahedron. We can use 3 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)))

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