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Edge Length of Dodecahedron given Circumsphere Radius Formula

GoEdge Length of Dodecahedron given Insphere Radius Formula

GoEdge Length of Dodecahedron given Total Surface Area Formula

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Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron. Check FAQs

l e = \frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})}

l_e - Edge Length of Dodecahedron?r_c - Circumsphere Radius of Dodecahedron?

Edge Length of Dodecahedron given Circumsphere Radius Example

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Here is how the Edge Length of Dodecahedron given Circumsphere Radius equation looks like with Values.

Here is how the Edge Length of Dodecahedron given Circumsphere Radius equation looks like with Units.

Here is how the Edge Length of Dodecahedron given Circumsphere Radius equation looks like.

9.991 = \frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})}

9.991m = \frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})}

9.991 = \frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})}

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3D Geometry » fx Edge Length of Dodecahedron given Circumsphere Radius

Edge Length of Dodecahedron given Circumsphere Radius Solution

Follow our step by step solution on how to calculate Edge Length of Dodecahedron given Circumsphere Radius?

FIRST Step Consider the formula

l e = \frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Substitute values of Variables

∴

l e = \frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

l e = \frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Evaluate

∴

l e = 9.99101851364652m

LAST Step Rounding Answer

∴

l e = 9.991m

Edge Length of Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Edge Length of Dodecahedron

Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Dodecahedron

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of 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 Edge Length of Dodecahedron

Go Edge Length of Dodecahedron given Insphere Radius

l e = \frac{2 \cdot r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Go Edge Length of Dodecahedron given Total Surface Area

l e = \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Edge Length of Dodecahedron given Volume

l e = {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

How to Evaluate Edge Length of Dodecahedron given Circumsphere Radius?

Edge Length of Dodecahedron given Circumsphere Radius evaluator uses Edge Length of Dodecahedron = (4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))) to evaluate the Edge Length of Dodecahedron, Edge Length of Dodecahedron given Circumsphere Radius formula is defined as the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron, and calculated using the circumsphere radius of the Dodecahedron. Edge Length of Dodecahedron is denoted by l_e symbol.

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

FAQs on Edge Length of Dodecahedron given Circumsphere Radius

What is the formula to find Edge Length of Dodecahedron given Circumsphere Radius?

The formula of Edge Length of Dodecahedron given Circumsphere Radius is expressed as Edge Length of Dodecahedron = (4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))). Here is an example- 9.991019 = (4*14)/(sqrt(3)*(1+sqrt(5))).

How to calculate Edge Length of Dodecahedron given Circumsphere Radius?

With Circumsphere Radius of Dodecahedron (r_c) we can find Edge Length of Dodecahedron given Circumsphere Radius using the formula - Edge Length of Dodecahedron = (4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Edge Length of Dodecahedron?

Here are the different ways to Calculate Edge Length of Dodecahedron-

Edge Length of Dodecahedron=(2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10)
Edge Length of Dodecahedron=sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Edge Length of Dodecahedron=((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)

Can the Edge Length of Dodecahedron given Circumsphere Radius be negative?

No, the Edge Length of Dodecahedron given Circumsphere Radius, measured in Length cannot be negative.

Which unit is used to measure Edge Length of Dodecahedron given Circumsphere Radius?

Edge Length of 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 Edge Length of Dodecahedron given Circumsphere Radius can be measured.

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