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Edge Length of Dodecahedron given Insphere 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{2 \cdot r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

l_e - Edge Length of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Edge Length of Dodecahedron given Insphere Radius Example

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

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

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

9.8786 = \frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

9.8786m = \frac{2 \cdot 11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

9.8786 = \frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

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Edge Length of Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

l e = 9.87861548475088m

LAST Step Rounding Answer

∴

l e = 9.8786m

Edge Length of Dodecahedron given Insphere 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

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere 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}}

How to Evaluate Edge Length of Dodecahedron given Insphere Radius?

Edge Length of Dodecahedron given Insphere Radius evaluator uses Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10) to evaluate the Edge Length of Dodecahedron, The Edge Length of Dodecahedron given Insphere 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 insphere radius of Dodecahedron. Edge Length of Dodecahedron is denoted by l_e symbol.

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

FAQs on Edge Length of Dodecahedron given Insphere Radius

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

The formula of Edge Length of Dodecahedron given Insphere Radius is expressed as Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10). Here is an example- 9.878615 = (2*11)/sqrt((25+(11*sqrt(5)))/10).

How to calculate Edge Length of Dodecahedron given Insphere Radius?

With Insphere Radius of Dodecahedron (r_i) we can find Edge Length of Dodecahedron given Insphere Radius using the formula - Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10). 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 Insphere Radius be negative?

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

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

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

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