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Pyramidal Height of Great Dodecahedron given Circumsphere Radius Formula

GoPyramidal Height of Great Dodecahedron Formula

GoPyramidal Height of Great Dodecahedron given Ridge Length Formula

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

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

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

Pyramidal Height of Great Dodecahedron given Circumsphere Radius Example

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

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

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

2.0869 = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}}

2.0869m = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

2.0869 = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}}

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Pyramidal Height of Great Dodecahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

h Pyramid = 2.08689345032874m

LAST Step Rounding Answer

∴

h Pyramid = 2.0869m

Pyramidal Height of Great Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

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

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

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 Pyramidal Height of Great Dodecahedron

Go Pyramidal Height of Great Dodecahedron

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot l e

Go Pyramidal Height of Great Dodecahedron given Ridge Length

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{2 \cdot l Ridge}{\sqrt{5} - 1}

Go Pyramidal Height of Great Dodecahedron given Total Surface Area

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

Go Pyramidal Height of Great Dodecahedron given Volume

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot {(\frac{4 \cdot V}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

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

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

FAQs on Pyramidal Height of Great Dodecahedron given Circumsphere Radius

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

The formula of Pyramidal Height of Great Dodecahedron given Circumsphere Radius is expressed as Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))). Here is an example- 2.086893 = (sqrt(3)*(3-sqrt(5)))/6*(4*9)/sqrt(10+(2*sqrt(5))).

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

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

What are the other ways to Calculate Pyramidal Height of Great Dodecahedron?

Here are the different ways to Calculate Pyramidal Height of Great Dodecahedron-

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)))))

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

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

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

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

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