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Surface to Volume Ratio of Icosahedron given Insphere Radius Formula

GoSurface to Volume Ratio of Icosahedron Formula

GoSurface to Volume Ratio of Icosahedron given Circumsphere Radius Formula

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

R A/V = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}

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

Surface to Volume Ratio of Icosahedron given Insphere Radius Example

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

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

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

0.4286 = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}

0.4286m⁻¹ = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}

0.4286 = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}

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Surface to Volume Ratio of Icosahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

R A/V = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}

Next Step Substitute values of Variables

∴

R A/V = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

R A/V = 0.428571428571429m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.4286m⁻¹

Surface to Volume Ratio of Icosahedron given Insphere Radius Formula Elements

Variables

Functions

Surface to Volume Ratio of Icosahedron

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

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Icosahedron

Insphere Radius of Icosahedron

Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron 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 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 Surface to Volume Ratio of Icosahedron

Go Surface to Volume Ratio of Icosahedron

R A/V = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot l e}

Go Surface to Volume Ratio of Icosahedron given Circumsphere Radius

R A/V = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}

Go Surface to Volume Ratio of Icosahedron given Midsphere Radius

R A/V = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{4 \cdot r m}{1 + \sqrt{5}})}

Go Surface to Volume Ratio of Icosahedron given Space Diagonal

R A/V = \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot (\frac{2 \cdot d Space}{\sqrt{10 + (2 \cdot \sqrt{5})}})}

How to Evaluate Surface to Volume Ratio of Icosahedron given Insphere Radius?

Surface to Volume Ratio of Icosahedron given Insphere Radius evaluator uses Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))) to evaluate the Surface to Volume Ratio of Icosahedron, The Surface to Volume Ratio of Icosahedron given Insphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is calculated using the insphere radius of the Icosahedron. Surface to Volume Ratio of Icosahedron is denoted by R_A/V symbol.

How to evaluate Surface to Volume Ratio of Icosahedron given Insphere Radius using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (r_i) and hit the calculate button.

FAQs on Surface to Volume Ratio of Icosahedron given Insphere Radius

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

The formula of Surface to Volume Ratio of Icosahedron given Insphere Radius is expressed as Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))). Here is an example- 0.428571 = (12*sqrt(3))/((3+sqrt(5))*((12*7)/(sqrt(3)*(3+sqrt(5))))).

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

With Insphere Radius of Icosahedron (r_i) we can find Surface to Volume Ratio of Icosahedron given Insphere Radius using the formula - Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))). This formula also uses Square Root (sqrt) function(s).

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

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

Surface to Volume Ratio of Icosahedron=(12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron)
Surface to Volume Ratio of Icosahedron=(12*sqrt(3))/((3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))))
Surface to Volume Ratio of Icosahedron=(12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5))))

Can the Surface to Volume Ratio of Icosahedron given Insphere Radius be negative?

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

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

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

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