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Space Diagonal of Icosahedron given Face Area 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 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{3}}}

d_Space - Space Diagonal of Icosahedron?A_Face - Face Area of Icosahedron?

Space Diagonal of Icosahedron given Face Area Example

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Here is how the Space Diagonal of Icosahedron given Face Area equation looks like with Values.

Here is how the Space Diagonal of Icosahedron given Face Area equation looks like with Units.

Here is how the Space Diagonal of Icosahedron given Face Area equation looks like.

19.3906 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

19.3906m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

19.3906 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

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Space Diagonal of Icosahedron given Face Area Solution

Follow our step by step solution on how to calculate Space Diagonal of Icosahedron given Face Area?

FIRST Step Consider the formula

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{3}}}

Next Step Substitute values of Variables

∴

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

Next Step Prepare to Evaluate

∴

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

Next Step Evaluate

∴

d Space = 19.3906452064276m

LAST Step Rounding Answer

∴

d Space = 19.3906m

Space Diagonal of Icosahedron given Face Area 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

Face Area of Icosahedron

The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area 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 Midsphere Radius

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

How to Evaluate Space Diagonal of Icosahedron given Face Area?

Space Diagonal of Icosahedron given Face Area evaluator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3)) to evaluate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Face Area formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the face area of the Icosahedron. Space Diagonal of Icosahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Icosahedron given Face Area

What is the formula to find Space Diagonal of Icosahedron given Face Area?

The formula of Space Diagonal of Icosahedron given Face Area is expressed as Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3)). Here is an example- 19.39065 = sqrt(10+(2*sqrt(5)))/2*sqrt((4*45)/sqrt(3)).

How to calculate Space Diagonal of Icosahedron given Face Area?

With Face Area of Icosahedron (A_Face) we can find Space Diagonal of Icosahedron given Face Area using the formula - Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((4*Face Area of Icosahedron)/sqrt(3)). 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)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5))

Can the Space Diagonal of Icosahedron given Face Area be negative?

No, the Space Diagonal of Icosahedron given Face Area, measured in Length cannot be negative.

Which unit is used to measure Space Diagonal of Icosahedron given Face Area?

Space Diagonal of Icosahedron given Face Area 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 Face Area can be measured.

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