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Edge Length of Dodecahedron given Midsphere Radius Formula

GoEdge Length of Dodecahedron given Circumsphere 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 m}{3 + \sqrt{5}}

l_e - Edge Length of Dodecahedron?r_m - Midsphere Radius of Dodecahedron?

Edge Length of Dodecahedron given Midsphere Radius Example

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

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

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

9.9311 = \frac{4 \cdot 13}{3 + \sqrt{5}}

9.9311m = \frac{4 \cdot 13m}{3 + \sqrt{5}}

9.9311 = \frac{4 \cdot 13}{3 + \sqrt{5}}

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Edge Length of Dodecahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

l e = \frac{4 \cdot r m}{3 + \sqrt{5}}

Next Step Substitute values of Variables

∴

l e = \frac{4 \cdot 13m}{3 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

l e = \frac{4 \cdot 13}{3 + \sqrt{5}}

Next Step Evaluate

∴

l e = 9.93111629250273m

LAST Step Rounding Answer

∴

l e = 9.9311m

Edge Length of Dodecahedron given Midsphere 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

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere 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 Circumsphere Radius

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

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}}

Go Edge Length of Dodecahedron given Face Area

l e = \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Edge Length of Dodecahedron given Midsphere Radius?

Edge Length of Dodecahedron given Midsphere Radius evaluator uses Edge Length of Dodecahedron = (4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)) to evaluate the Edge Length of Dodecahedron, The Edge Length of Dodecahedron given Midsphere 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 midsphere radius of Dodecahedron. Edge Length of Dodecahedron is denoted by l_e symbol.

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

FAQs on Edge Length of Dodecahedron given Midsphere Radius

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

The formula of Edge Length of Dodecahedron given Midsphere Radius is expressed as Edge Length of Dodecahedron = (4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)). Here is an example- 9.931116 = (4*13)/(3+sqrt(5)).

How to calculate Edge Length of Dodecahedron given Midsphere Radius?

With Midsphere Radius of Dodecahedron (r_m) we can find Edge Length of Dodecahedron given Midsphere Radius using the formula - Edge Length of Dodecahedron = (4*Midsphere Radius of Dodecahedron)/(3+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=(4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
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 Midsphere Radius be negative?

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

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

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

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