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Surface to Volume Ratio of Dodecahedron given Face Diagonal Formula

GoSurface to Volume Ratio of Dodecahedron Formula

GoSurface to Volume Ratio of Dodecahedron given Volume Formula

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

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

R_A/V - Surface to Volume Ratio of Dodecahedron?d_Face - Face Diagonal of Dodecahedron?

Surface to Volume Ratio of Dodecahedron given Face Diagonal Example

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

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

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

0.2725 = \frac{1 + \sqrt{5}}{16} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

0.2725m⁻¹ = \frac{1 + \sqrt{5}}{16m} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

0.2725 = \frac{1 + \sqrt{5}}{16} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

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Surface to Volume Ratio of Dodecahedron given Face Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R A/V = \frac{1 + \sqrt{5}}{16m} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

Next Step Prepare to Evaluate

∴

R A/V = \frac{1 + \sqrt{5}}{16} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

Next Step Evaluate

∴

R A/V = 0.27245344800201m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.2725m⁻¹

Surface to Volume Ratio of Dodecahedron given Face Diagonal Formula Elements

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Functions

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

Face Diagonal of Dodecahedron

The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.

Symbol: d_Face

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Face Diagonal 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 Surface to Volume Ratio of Dodecahedron

Go Surface to Volume Ratio of Dodecahedron

R A/V = \frac{12 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{l e \cdot (15 + (7 \cdot \sqrt{5}))}

Go Surface to Volume Ratio of Dodecahedron given Volume

R A/V = {(\frac{15 + (7 \cdot \sqrt{5})}{4 \cdot V})}^{\frac{1}{3}} \cdot \frac{12 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

Go Surface to Volume Ratio of Dodecahedron given Total Surface Area

R A/V = \sqrt{\frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{TSA}} \cdot \frac{12 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

Go Surface to Volume Ratio of Dodecahedron given Face Area

R A/V = \sqrt{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{4 \cdot A Face}} \cdot \frac{12 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{15 + (7 \cdot \sqrt{5})}

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

Surface to Volume Ratio of Dodecahedron given Face Diagonal evaluator uses Surface to Volume Ratio of Dodecahedron = (1+sqrt(5))/Face Diagonal of Dodecahedron*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5))) to evaluate the Surface to Volume Ratio of Dodecahedron, The Surface to Volume Ratio of Dodecahedron given Face Diagonal formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the face diagonal of the Dodecahedron. Surface to Volume Ratio of Dodecahedron is denoted by R_A/V symbol.

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

FAQs on Surface to Volume Ratio of Dodecahedron given Face Diagonal

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

The formula of Surface to Volume Ratio of Dodecahedron given Face Diagonal is expressed as Surface to Volume Ratio of Dodecahedron = (1+sqrt(5))/Face Diagonal of Dodecahedron*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5))). Here is an example- 0.272453 = (1+sqrt(5))/16*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5))).

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

With Face Diagonal of Dodecahedron (d_Face) we can find Surface to Volume Ratio of Dodecahedron given Face Diagonal using the formula - Surface to Volume Ratio of Dodecahedron = (1+sqrt(5))/Face Diagonal of Dodecahedron*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Surface to Volume Ratio of Dodecahedron?

Here are the different ways to Calculate Surface to Volume Ratio of Dodecahedron-

Surface to Volume Ratio of Dodecahedron=(12*sqrt(25+(10*sqrt(5))))/(Edge Length of Dodecahedron*(15+(7*sqrt(5))))
Surface to Volume Ratio of Dodecahedron=((15+(7*sqrt(5)))/(4*Volume of Dodecahedron))^(1/3)*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron=sqrt((3*sqrt(25+(10*sqrt(5))))/Total Surface Area of Dodecahedron)*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))

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

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

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

Surface to Volume Ratio of Dodecahedron given Face Diagonal is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Dodecahedron given Face Diagonal can be measured.

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