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Insphere Radius of Icosahedron given Surface to Volume Ratio Formula

GoInsphere Radius of Icosahedron Formula

GoInsphere Radius of Icosahedron given Total Surface Area Formula

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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. Check FAQs

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

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

Insphere Radius of Icosahedron given Surface to Volume Ratio Example

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

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

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

7.5 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4}

7.5m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4m⁻¹}

7.5 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4}

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Insphere Radius of Icosahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4m⁻¹}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4}

LAST Step Evaluate

∴

r i = 7.5m

Insphere Radius of Icosahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

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

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

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 Insphere Radius of Icosahedron

Go Insphere Radius of Icosahedron

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot l e

Go Insphere Radius of Icosahedron given Total Surface Area

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}}

Go Insphere Radius of Icosahedron given Circumsphere Radius

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Go Insphere Radius of Icosahedron given Midsphere Radius

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{4 \cdot r m}{1 + \sqrt{5}}

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

Insphere Radius of Icosahedron given Surface to Volume Ratio evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron) to evaluate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the surface to volume ratio of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron given Surface to Volume Ratio

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

The formula of Insphere Radius of Icosahedron given Surface to Volume Ratio is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). Here is an example- 7.5 = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*0.4).

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

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

What are the other ways to Calculate Insphere Radius of Icosahedron?

Here are the different ways to Calculate Insphere Radius of Icosahedron-

Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron
Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*(4*Circumsphere Radius of Icosahedron)/sqrt(10+(2*sqrt(5)))

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

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

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

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

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