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Space Diagonal of Dodecahedron given Surface to Volume Ratio Formula

GoSpace Diagonal of Dodecahedron Formula

GoSpace Diagonal of Dodecahedron given Volume 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 (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{R A/V \cdot (15 + (7 \cdot \sqrt{5}))}

d_Space - Space Diagonal of Dodecahedron?R_A/V - Surface to Volume Ratio of Dodecahedron?

Space Diagonal of Dodecahedron given Surface to Volume Ratio Example

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

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

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

25.1682 = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

25.1682m = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3m⁻¹ \cdot (15 + (7 \cdot \sqrt{5}))}

25.1682 = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

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Space Diagonal of Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{R A/V \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Substitute values of Variables

∴

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3m⁻¹ \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Prepare to Evaluate

∴

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Evaluate

∴

d Space = 25.1681714472964m

LAST Step Rounding Answer

∴

d Space = 25.1682m

Space Diagonal of Dodecahedron given Surface to Volume Ratio 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

Surface to Volume Ratio of Dodecahedron

The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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 Volume

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

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})}}}

How to Evaluate Space Diagonal of Dodecahedron given Surface to Volume Ratio?

Space Diagonal of Dodecahedron given Surface to Volume Ratio evaluator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))) to evaluate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Surface to Volume Ratio formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using surface to volume ratio of Dodecahedron. Space Diagonal of Dodecahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Dodecahedron given Surface to Volume Ratio

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

The formula of Space Diagonal of Dodecahedron given Surface to Volume Ratio is expressed as Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). Here is an example- 25.16817 = sqrt(3)*(1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5)))).

How to calculate Space Diagonal of Dodecahedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Dodecahedron (R_A/V) we can find Space Diagonal of Dodecahedron given Surface to Volume Ratio using the formula - Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). 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*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Space Diagonal of Dodecahedron=sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

Can the Space Diagonal of Dodecahedron given Surface to Volume Ratio be negative?

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

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

Space Diagonal of Dodecahedron given Surface to Volume Ratio 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 Surface to Volume Ratio can be measured.

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