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Circumsphere Radius of Great Stellated Dodecahedron Formula

GoCircumsphere Radius of Great Stellated Dodecahedron given Ridge Length Formula

GoCircumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord Formula

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Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere. Check FAQs

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot l e

r_c - Circumradius of Great Stellated Dodecahedron?l_e - Edge Length of Great Stellated Dodecahedron?

Circumsphere Radius of Great Stellated Dodecahedron Example

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Here is how the Circumsphere Radius of Great Stellated Dodecahedron equation looks like with Values.

Here is how the Circumsphere Radius of Great Stellated Dodecahedron equation looks like with Units.

Here is how the Circumsphere Radius of Great Stellated Dodecahedron equation looks like.

22.6728 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot 10

22.6728m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot 10m

22.6728 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot 10

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Circumsphere Radius of Great Stellated Dodecahedron Solution

Follow our step by step solution on how to calculate Circumsphere Radius of Great Stellated Dodecahedron?

FIRST Step Consider the formula

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot l e

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r c = 22.6728394222851m

LAST Step Rounding Answer

∴

r c = 22.6728m

Circumsphere Radius of Great Stellated Dodecahedron Formula Elements

Variables

Functions

Circumradius of Great Stellated Dodecahedron

Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Great Stellated Dodecahedron

Edge Length of Great Stellated Dodecahedron

Edge Length of Great Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Great Stellated 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 Circumradius of Great Stellated Dodecahedron

Go Circumsphere Radius of Great Stellated Dodecahedron given Ridge Length

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{2} \cdot \frac{1 \cdot l Ridge}{1 + \sqrt{5}}

Go Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \frac{l c(Pentagram)}{2 + \sqrt{5}}

Go Circumsphere Radius of Great Stellated Dodecahedron given Pyramidal Height

r c = \frac{3 \cdot h Pyramid}{2}

Go Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

How to Evaluate Circumsphere Radius of Great Stellated Dodecahedron?

Circumsphere Radius of Great Stellated Dodecahedron evaluator uses Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Edge Length of Great Stellated Dodecahedron to evaluate the Circumradius of Great Stellated Dodecahedron, Circumsphere Radius of Great Stellated Dodecahedron formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere. Circumradius of Great Stellated Dodecahedron is denoted by r_c symbol.

How to evaluate Circumsphere Radius of Great Stellated Dodecahedron using this online evaluator? To use this online evaluator for Circumsphere Radius of Great Stellated Dodecahedron, enter Edge Length of Great Stellated Dodecahedron (l_e) and hit the calculate button.

FAQs on Circumsphere Radius of Great Stellated Dodecahedron

What is the formula to find Circumsphere Radius of Great Stellated Dodecahedron?

The formula of Circumsphere Radius of Great Stellated Dodecahedron is expressed as Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Edge Length of Great Stellated Dodecahedron. Here is an example- 22.67284 = (sqrt(3)*(3+sqrt(5)))/4*10.

How to calculate Circumsphere Radius of Great Stellated Dodecahedron?

With Edge Length of Great Stellated Dodecahedron (l_e) we can find Circumsphere Radius of Great Stellated Dodecahedron using the formula - Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*Edge Length of Great Stellated Dodecahedron. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Great Stellated Dodecahedron?

Here are the different ways to Calculate Circumradius of Great Stellated Dodecahedron-

Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/2*(1*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))
Circumradius of Great Stellated Dodecahedron=(3*Pyramidal Height of Great Stellated Dodecahedron)/2

Can the Circumsphere Radius of Great Stellated Dodecahedron be negative?

No, the Circumsphere Radius of Great Stellated Dodecahedron, measured in Length cannot be negative.

Which unit is used to measure Circumsphere Radius of Great Stellated Dodecahedron?

Circumsphere Radius of Great Stellated Dodecahedron 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 Stellated Dodecahedron can be measured.

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