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Space Diagonal of Icosahedron given Midsphere Radius Formula

GoSpace Diagonal of Icosahedron given Circumsphere Radius Formula

GoSpace Diagonal of Icosahedron given Insphere Radius Formula

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The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron. Check FAQs

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot r m}{1 + \sqrt{5}}

d_Space - Space Diagonal of Icosahedron?r_m - Midsphere Radius of Icosahedron?

Space Diagonal of Icosahedron given Midsphere Radius Example

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Here is how the Space Diagonal of Icosahedron given Midsphere Radius equation looks like with Values.

Here is how the Space Diagonal of Icosahedron given Midsphere Radius equation looks like with Units.

Here is how the Space Diagonal of Icosahedron given Midsphere Radius equation looks like.

18.8091 = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot 8}{1 + \sqrt{5}}

18.8091m = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot 8m}{1 + \sqrt{5}}

18.8091 = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot 8}{1 + \sqrt{5}}

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Space Diagonal of Icosahedron given Midsphere Radius Solution

Follow our step by step solution on how to calculate Space Diagonal of Icosahedron given Midsphere Radius?

FIRST Step Consider the formula

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot r m}{1 + \sqrt{5}}

Next Step Substitute values of Variables

∴

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot 8m}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot 8}{1 + \sqrt{5}}

Next Step Evaluate

∴

d Space = 18.8091280733591m

LAST Step Rounding Answer

∴

d Space = 18.8091m

Space Diagonal of Icosahedron given Midsphere Radius Formula Elements

Variables

Functions

Space Diagonal of Icosahedron

The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of Icosahedron

Midsphere Radius of Icosahedron

The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron 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 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 Space Diagonal of Icosahedron

Go Space Diagonal of Icosahedron given Circumsphere Radius

d Space = 2 \cdot r c

Go Space Diagonal of Icosahedron given Insphere Radius

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

Go Space Diagonal of Icosahedron given Surface to Volume Ratio

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot R A/V}

Go Space Diagonal of Icosahedron given Total Surface Area

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}}

How to Evaluate Space Diagonal of Icosahedron given Midsphere Radius?

Space Diagonal of Icosahedron given Midsphere Radius evaluator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5)) to evaluate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Midsphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the midsphere radius of the Icosahedron. Space Diagonal of Icosahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Icosahedron given Midsphere Radius

What is the formula to find Space Diagonal of Icosahedron given Midsphere Radius?

The formula of Space Diagonal of Icosahedron given Midsphere Radius is expressed as Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5)). Here is an example- 18.80913 = sqrt(10+(2*sqrt(5)))*(2*8)/(1+sqrt(5)).

How to calculate Space Diagonal of Icosahedron given Midsphere Radius?

With Midsphere Radius of Icosahedron (r_m) we can find Space Diagonal of Icosahedron given Midsphere Radius using the formula - Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Space Diagonal of Icosahedron?

Here are the different ways to Calculate Space Diagonal of Icosahedron-

Space Diagonal of Icosahedron=2*Circumsphere Radius of Icosahedron
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))*(6*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

Can the Space Diagonal of Icosahedron given Midsphere Radius be negative?

No, the Space Diagonal of Icosahedron given Midsphere Radius, measured in Length cannot be negative.

Which unit is used to measure Space Diagonal of Icosahedron given Midsphere Radius?

Space Diagonal of Icosahedron 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 Space Diagonal of Icosahedron given Midsphere Radius can be measured.

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