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Space Diagonal of Icosahedron given Volume Formula

GoSpace Diagonal of Icosahedron Formula

GoSpace Diagonal of Icosahedron given Lateral 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 {(\frac{\frac{12}{5} \cdot V}{3 + \sqrt{5}})}^{\frac{1}{3}}

d_Space - Space Diagonal of Icosahedron?V - Volume of Icosahedron?

Space Diagonal of Icosahedron given Volume Example

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

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

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

19.0742 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{\frac{12}{5} \cdot 2200}{3 + \sqrt{5}})}^{\frac{1}{3}}

19.0742m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{\frac{12}{5} \cdot 2200m³}{3 + \sqrt{5}})}^{\frac{1}{3}}

19.0742 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{\frac{12}{5} \cdot 2200}{3 + \sqrt{5}})}^{\frac{1}{3}}

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Space Diagonal of Icosahedron given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{\frac{12}{5} \cdot 2200m³}{3 + \sqrt{5}})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{\frac{12}{5} \cdot 2200}{3 + \sqrt{5}})}^{\frac{1}{3}}

Next Step Evaluate

∴

d Space = 19.0741797063212m

LAST Step Rounding Answer

∴

d Space = 19.0742m

Space Diagonal of Icosahedron given Volume 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

Volume of Icosahedron

Volume of Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Icosahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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

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

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}}}

How to Evaluate Space Diagonal of Icosahedron given Volume?

Space Diagonal of Icosahedron given Volume evaluator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3) to evaluate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Volume formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the volume of the Icosahedron. Space Diagonal of Icosahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Icosahedron given Volume

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

The formula of Space Diagonal of Icosahedron given Volume is expressed as Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3). Here is an example- 19.07418 = sqrt(10+(2*sqrt(5)))/2*((12/5*2200)/(3+sqrt(5)))^(1/3).

How to calculate Space Diagonal of Icosahedron given Volume?

With Volume of Icosahedron (V) we can find Space Diagonal of Icosahedron given Volume using the formula - Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3). 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=sqrt(10+(2*sqrt(5)))/2*Edge Length 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)))

Can the Space Diagonal of Icosahedron given Volume be negative?

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

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

Space Diagonal of Icosahedron given Volume 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 Volume can be measured.

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