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Space Diagonal of Dodecahedron given Volume Formula

GoSpace Diagonal of Dodecahedron Formula

GoSpace Diagonal of Dodecahedron given Total Surface Area Formula

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

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

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

Space Diagonal of Dodecahedron given Volume Example

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

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

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

28.0701 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

28.0701m = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

28.0701 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

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Space Diagonal of Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Evaluate

∴

d Space = 28.0700586570594m

LAST Step Rounding Answer

∴

d Space = 28.0701m

Space Diagonal of Dodecahedron given Volume Formula Elements

Variables

Functions

Space Diagonal of Dodecahedron

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

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of Dodecahedron

Volume of Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Dodecahedron

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 Dodecahedron

Go Space Diagonal of Dodecahedron

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{l e}{2}

Go Space Diagonal of Dodecahedron given Total Surface Area

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Space Diagonal of Dodecahedron given Face Area

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot A Face}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Space Diagonal of Dodecahedron given Circumsphere Radius

d Space = 2 \cdot r c

How to Evaluate Space Diagonal of Dodecahedron given Volume?

Space Diagonal of Dodecahedron given Volume evaluator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3) to evaluate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Volume formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using volume of Dodecahedron. Space Diagonal of Dodecahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Dodecahedron given Volume

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

The formula of Space Diagonal of Dodecahedron given Volume is expressed as Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). Here is an example- 28.07006 = sqrt(3)*(1+sqrt(5))/2*((4*7700)/(15+(7*sqrt(5))))^(1/3).

How to calculate Space Diagonal of Dodecahedron given Volume?

With Volume of Dodecahedron (V) we can find Space Diagonal of Dodecahedron given Volume using the formula - Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). This formula also uses Square Root (sqrt) function(s).

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

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

Space Diagonal of Dodecahedron=sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
Space Diagonal of Dodecahedron=sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron=sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))

Can the Space Diagonal of Dodecahedron given Volume be negative?

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

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

Space Diagonal of Dodecahedron 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 Dodecahedron given Volume can be measured.

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