Pyramidal Height 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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✖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 given Circumsphere Radius [h_Pyramid]

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Pyramidal Height of Great Dodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

h_Pyramid = (sqrt(3)*(3-sqrt(5)))/6*(4*r_c)/sqrt(10+(2*sqrt(5))) --> (sqrt(3)*(3-sqrt(5)))/6*(4*9)/sqrt(10+(2*sqrt(5)))

Evaluating ... ...

h_Pyramid = 2.08689345032874

STEP 3: Convert Result to Output's Unit

2.08689345032874 Meter --> No Conversion Required

FINAL ANSWER

2.08689345032874 ≈ 2.086893 Meter <-- Pyramidal Height of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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< Pyramidal Height of Great Dodecahedron Calculators

Pyramidal Height of Great Dodecahedron given Total Surface Area

LaTeX Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

Pyramidal Height of Great Dodecahedron given Circumsphere Radius

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

Pyramidal Height of Great Dodecahedron given Ridge Length

LaTeX Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)

Pyramidal Height of Great Dodecahedron

LaTeX Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*Edge Length of Great Dodecahedron

Pyramidal Height of Great Dodecahedron given Circumsphere Radius Formula

LaTeX Go

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

Pyramidal Height of Great Dodecahedron given Circumsphere Radius calculator uses Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))) to calculate the Pyramidal Height of Great Dodecahedron, Pyramidal Height of Great Dodecahedron given Circumsphere Radius formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its circumsphere radius. Pyramidal Height of Great Dodecahedron is denoted by h_Pyramid symbol.

How to calculate Pyramidal Height of Great Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Pyramidal Height of Great Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Great Dodecahedron (r_c) and hit the calculate button. Here is how the Pyramidal Height of Great Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 2.086893 = (sqrt(3)*(3-sqrt(5)))/6*(4*9)/sqrt(10+(2*sqrt(5))).

FAQ

What is Pyramidal Height of Great Dodecahedron given Circumsphere Radius?

Pyramidal Height of Great Dodecahedron given Circumsphere Radius formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its circumsphere radius and is represented as h_Pyramid = (sqrt(3)*(3-sqrt(5)))/6*(4*r_c)/sqrt(10+(2*sqrt(5))) or Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))). 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 Pyramidal Height of Great Dodecahedron given Circumsphere Radius?

Pyramidal Height of Great Dodecahedron given Circumsphere Radius formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its circumsphere radius is calculated using Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))). To calculate Pyramidal Height 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 Pyramidal Height of Great Dodecahedron?

In this formula, Pyramidal Height of Great Dodecahedron uses Circumsphere Radius of Great Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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