Circumsphere Radius of Great Dodecahedron given Pyramidal Height Calculator

✖Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.ⓘ Pyramidal Height of Great Dodecahedron [h_Pyramid]

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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 Pyramidal Height [r_c]

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Circumsphere Radius of Great Dodecahedron given Pyramidal Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))
r_c = sqrt(10+(2*sqrt(5)))/4*(6*h_Pyramid)/(sqrt(3)*(3-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.
Pyramidal Height of Great Dodecahedron - (Measured in Meter) - Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pyramidal Height of Great Dodecahedron: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(10+(2*sqrt(5)))/4*(6*h_Pyramid)/(sqrt(3)*(3-sqrt(5))) --> sqrt(10+(2*sqrt(5)))/4*(6*2)/(sqrt(3)*(3-sqrt(5)))

Evaluating ... ...

r_c = 8.62526067019117

STEP 3: Convert Result to Output's Unit

8.62526067019117 Meter --> No Conversion Required

FINAL ANSWER

8.62526067019117 ≈ 8.625261 Meter <-- Circumsphere Radius of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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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 Pyramidal Height Formula

LaTeX Go

Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))
r_c = sqrt(10+(2*sqrt(5)))/4*(6*h_Pyramid)/(sqrt(3)*(3-sqrt(5)))

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 Pyramidal Height?

Circumsphere Radius of Great Dodecahedron given Pyramidal Height calculator uses Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))) to calculate the Circumsphere Radius of Great Dodecahedron, The Circumsphere Radius of Great Dodecahedron given Pyramidal Height 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 pyramidal height. Circumsphere Radius of Great Dodecahedron is denoted by r_c symbol.

How to calculate Circumsphere Radius of Great Dodecahedron given Pyramidal Height using this online calculator? To use this online calculator for Circumsphere Radius of Great Dodecahedron given Pyramidal Height, enter Pyramidal Height of Great Dodecahedron (h_Pyramid) and hit the calculate button. Here is how the Circumsphere Radius of Great Dodecahedron given Pyramidal Height calculation can be explained with given input values -> 8.625261 = sqrt(10+(2*sqrt(5)))/4*(6*2)/(sqrt(3)*(3-sqrt(5))).

FAQ

What is Circumsphere Radius of Great Dodecahedron given Pyramidal Height?

The Circumsphere Radius of Great Dodecahedron given Pyramidal Height 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 pyramidal height and is represented as r_c = sqrt(10+(2*sqrt(5)))/4*(6*h_Pyramid)/(sqrt(3)*(3-sqrt(5))) or Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))). Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

How to calculate Circumsphere Radius of Great Dodecahedron given Pyramidal Height?

The Circumsphere Radius of Great Dodecahedron given Pyramidal Height 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 pyramidal height is calculated using Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))). To calculate Circumsphere Radius of Great Dodecahedron given Pyramidal Height, you need Pyramidal Height of Great Dodecahedron (h_Pyramid). With our tool, you need to enter the respective value for Pyramidal Height 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 Pyramidal Height 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*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

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