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Edge Length of Icosahedron given Insphere Radius Formula

GoEdge Length of Icosahedron given Surface to Volume Ratio Formula

GoEdge Length of Icosahedron given Circumsphere Radius Formula

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

l e = \frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

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

Edge Length of Icosahedron given Insphere Radius Example

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

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

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

9.2622 = \frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

9.2622m = \frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})}

9.2622 = \frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

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Edge Length of Icosahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

l e = \frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Substitute values of Variables

∴

l e = \frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

l e = \frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Evaluate

∴

l e = 9.26218353549451m

LAST Step Rounding Answer

∴

l e = 9.2622m

Edge Length of Icosahedron given Insphere Radius Formula Elements

Variables

Functions

Edge Length of Icosahedron

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

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Icosahedron

Insphere Radius of Icosahedron

Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron 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 Icosahedron

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 Icosahedron

Go Edge Length of Icosahedron given Surface to Volume Ratio

l e = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot R A/V}

Go Edge Length of Icosahedron given Circumsphere Radius

l e = \frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Go Edge Length of Icosahedron given Midsphere Radius

l e = \frac{4 \cdot r m}{1 + \sqrt{5}}

Go Edge Length of Icosahedron given Space Diagonal

l e = \frac{2 \cdot d Space}{\sqrt{10 + (2 \cdot \sqrt{5})}}

How to Evaluate Edge Length of Icosahedron given Insphere Radius?

Edge Length of Icosahedron given Insphere Radius evaluator uses Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to evaluate the Edge Length of Icosahedron, The Edge Length of Icosahedron given Insphere Radius formula is defined as the length of any of the edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron and is calculated using the insphere radius of the Icosahedron. Edge Length of Icosahedron is denoted by l_e symbol.

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

FAQs on Edge Length of Icosahedron given Insphere Radius

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

The formula of Edge Length of Icosahedron given Insphere Radius is expressed as Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). Here is an example- 9.262184 = (12*7)/(sqrt(3)*(3+sqrt(5))).

How to calculate Edge Length of Icosahedron given Insphere Radius?

With Insphere Radius of Icosahedron (r_i) we can find Edge Length of Icosahedron given Insphere Radius using the formula - Edge Length of Icosahedron = (12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). This formula also uses Square Root (sqrt) function(s).

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

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

Edge Length of Icosahedron=(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Edge Length of Icosahedron=(4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Edge Length of Icosahedron=(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))

Can the Edge Length of Icosahedron given Insphere Radius be negative?

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

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

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

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