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Space Diagonal of Icosahedron Formula

GoSpace Diagonal of Icosahedron given Lateral Surface Area Formula

GoSpace Diagonal of Icosahedron given Total Surface Area 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 l e

d_Space - Space Diagonal of Icosahedron?l_e - Edge Length of Icosahedron?

Space Diagonal of Icosahedron Example

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With units

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

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

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

19.0211 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot 10

19.0211m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot 10m

19.0211 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot 10

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Space Diagonal of Icosahedron Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

d Space = 19.0211303259031m

LAST Step Rounding Answer

∴

d Space = 19.0211m

Space Diagonal of Icosahedron 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

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

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 Lateral Surface Area

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2 \cdot LSA}{9 \cdot \sqrt{3}}}

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}}}

Go Space Diagonal of Icosahedron given Volume

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{\frac{12}{5} \cdot V}{3 + \sqrt{5}})}^{\frac{1}{3}}

How to Evaluate Space Diagonal of Icosahedron?

Space Diagonal of Icosahedron evaluator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*Edge Length of Icosahedron to evaluate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron. Space Diagonal of Icosahedron is denoted by d_Space symbol.

How to evaluate Space Diagonal of Icosahedron using this online evaluator? To use this online evaluator for Space Diagonal of Icosahedron, enter Edge Length of Icosahedron (l_e) and hit the calculate button.

FAQs on Space Diagonal of Icosahedron

What is the formula to find Space Diagonal of Icosahedron?

The formula of Space Diagonal of Icosahedron is expressed as Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*Edge Length of Icosahedron. Here is an example- 19.02113 = sqrt(10+(2*sqrt(5)))/2*10.

How to calculate Space Diagonal of Icosahedron?

With Edge Length of Icosahedron (l_e) we can find Space Diagonal of Icosahedron using the formula - Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*Edge Length of Icosahedron. 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=sqrt(10+(2*sqrt(5)))/2*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)

Can the Space Diagonal of Icosahedron be negative?

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

Which unit is used to measure Space Diagonal of Icosahedron?

Space Diagonal of Icosahedron 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 can be measured.

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