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Circumsphere Radius of Great Dodecahedron given Pyramidal Height Formula

GoCircumsphere Radius of Great Dodecahedron Formula

GoCircumsphere Radius of Great Dodecahedron given Ridge Length Formula

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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. Check FAQs

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 - \sqrt{5})}

r_c - Circumsphere Radius of Great Dodecahedron?h_Pyramid - Pyramidal Height of Great Dodecahedron?

Circumsphere Radius of Great Dodecahedron given Pyramidal Height Example

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Here is how the Circumsphere Radius of Great Dodecahedron given Pyramidal Height equation looks like with Values.

Here is how the Circumsphere Radius of Great Dodecahedron given Pyramidal Height equation looks like with Units.

Here is how the Circumsphere Radius of Great Dodecahedron given Pyramidal Height equation looks like.

8.6253 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot 2}{\sqrt{3} \cdot (3 - \sqrt{5})}

8.6253m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot 2m}{\sqrt{3} \cdot (3 - \sqrt{5})}

8.6253 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot 2}{\sqrt{3} \cdot (3 - \sqrt{5})}

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Circumsphere Radius of Great Dodecahedron given Pyramidal Height Solution

Follow our step by step solution on how to calculate Circumsphere Radius of Great Dodecahedron given Pyramidal Height?

FIRST Step Consider the formula

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 - \sqrt{5})}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot 2m}{\sqrt{3} \cdot (3 - \sqrt{5})}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot 2}{\sqrt{3} \cdot (3 - \sqrt{5})}

Next Step Evaluate

∴

r c = 8.62526067019117m

LAST Step Rounding Answer

∴

r c = 8.6253m

Circumsphere Radius of Great Dodecahedron given Pyramidal Height Formula Elements

Variables

Functions

Circumsphere Radius of Great Dodecahedron

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.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Great Dodecahedron

Pyramidal Height of Great Dodecahedron

Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

Symbol: h_Pyramid

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Pyramidal Height of Great Dodecahedron

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.

Syntax: sqrt(Number)

Other Formulas to find Circumsphere Radius of Great Dodecahedron

Go Circumsphere Radius of Great Dodecahedron

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot l e

Go Circumsphere Radius of Great Dodecahedron given Ridge Length

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot l Ridge}{\sqrt{5} - 1}

Go Circumsphere Radius of Great Dodecahedron given Total Surface Area

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

Go Circumsphere Radius of Great Dodecahedron given Volume

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot V}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

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

Circumsphere Radius of Great Dodecahedron given Pyramidal Height evaluator uses Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))) to evaluate 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 evaluate Circumsphere Radius of Great Dodecahedron given Pyramidal Height using this online evaluator? To use this online evaluator for Circumsphere Radius of Great Dodecahedron given Pyramidal Height, enter Pyramidal Height of Great Dodecahedron (h_Pyramid) and hit the calculate button.

FAQs on Circumsphere Radius of Great Dodecahedron given Pyramidal Height

What is the formula to find Circumsphere Radius of Great Dodecahedron given Pyramidal Height?

The formula of Circumsphere Radius of Great Dodecahedron given Pyramidal Height is expressed as Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))). Here is an example- 8.625261 = sqrt(10+(2*sqrt(5)))/4*(6*2)/(sqrt(3)*(3-sqrt(5))).

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

With Pyramidal Height of Great Dodecahedron (h_Pyramid) we can find Circumsphere Radius of Great Dodecahedron given Pyramidal Height using the formula - Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumsphere Radius of Great Dodecahedron?

Here are the different ways to Calculate Circumsphere Radius of Great Dodecahedron-

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)))))

Can the Circumsphere Radius of Great Dodecahedron given Pyramidal Height be negative?

No, the Circumsphere Radius of Great Dodecahedron given Pyramidal Height, measured in Length cannot be negative.

Which unit is used to measure Circumsphere Radius of Great Dodecahedron given Pyramidal Height?

Circumsphere Radius of Great Dodecahedron given Pyramidal Height is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumsphere Radius of Great Dodecahedron given Pyramidal Height can be measured.

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