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Surface to Volume Ratio of Dodecahedron given Insphere Radius 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 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{r i \cdot (15 + (7 \cdot \sqrt{5}))}

R_A/V - Surface to Volume Ratio of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Surface to Volume Ratio of Dodecahedron given Insphere Radius Example

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

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

Here is how the Surface to Volume Ratio of Dodecahedron given Insphere Radius equation looks like.

0.2727 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{11 \cdot (15 + (7 \cdot \sqrt{5}))}

0.2727m⁻¹ = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{11m \cdot (15 + (7 \cdot \sqrt{5}))}

0.2727 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{11 \cdot (15 + (7 \cdot \sqrt{5}))}

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Surface to Volume Ratio of Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

R A/V = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{r i \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Substitute values of Variables

∴

R A/V = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{11m \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Prepare to Evaluate

∴

R A/V = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{11 \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Evaluate

∴

R A/V = 0.272727272727273m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.2727m⁻¹

Surface to Volume Ratio of Dodecahedron given Insphere Radius Formula Elements

Variables

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

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius 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 Insphere Radius?

Surface to Volume Ratio of Dodecahedron given Insphere Radius evaluator uses Surface to Volume Ratio of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Insphere Radius of Dodecahedron*(15+(7*sqrt(5)))) to evaluate the Surface to Volume Ratio of Dodecahedron, The Surface to Volume Ratio of Dodecahedron given Insphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the insphere radius 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 Insphere Radius using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Dodecahedron given Insphere Radius, enter Insphere Radius of Dodecahedron (r_i) and hit the calculate button.

FAQs on Surface to Volume Ratio of Dodecahedron given Insphere Radius

What is the formula to find Surface to Volume Ratio of Dodecahedron given Insphere Radius?

The formula of Surface to Volume Ratio of Dodecahedron given Insphere Radius is expressed as Surface to Volume Ratio of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Insphere Radius of Dodecahedron*(15+(7*sqrt(5)))). Here is an example- 0.272727 = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(11*(15+(7*sqrt(5)))).

How to calculate Surface to Volume Ratio of Dodecahedron given Insphere Radius?

With Insphere Radius of Dodecahedron (r_i) we can find Surface to Volume Ratio of Dodecahedron given Insphere Radius using the formula - Surface to Volume Ratio of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Insphere Radius of Dodecahedron*(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 Insphere Radius be negative?

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

Which unit is used to measure Surface to Volume Ratio of Dodecahedron given Insphere Radius?

Surface to Volume Ratio of Dodecahedron given Insphere Radius 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 Insphere Radius can be measured.

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