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Circumsphere Radius of Icosahedron given Surface to Volume Ratio Formula

GoCircumsphere Radius of Icosahedron Formula

GoCircumsphere Radius of Icosahedron given Insphere Radius Formula

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Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere. Check FAQs

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

r_c - Circumsphere Radius of Icosahedron?R_A/V - Surface to Volume Ratio of Icosahedron?

Circumsphere Radius of Icosahedron given Surface to Volume Ratio Example

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

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

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

9.4381 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4}

9.4381m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4m⁻¹}

9.4381 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4}

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Circumsphere Radius of Icosahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4m⁻¹}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot 0.4}

Next Step Evaluate

∴

r c = 9.43806429273614m

LAST Step Rounding Answer

∴

r c = 9.4381m

Circumsphere Radius of Icosahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Circumsphere Radius of Icosahedron

Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere 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 Circumsphere Radius of Icosahedron

Go Circumsphere Radius of Icosahedron

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot l e

Go Circumsphere Radius of Icosahedron given Insphere Radius

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

Go Circumsphere Radius of Icosahedron given Midsphere Radius

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{4 \cdot r m}{1 + \sqrt{5}}

Go Circumsphere Radius of Icosahedron given Volume

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

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

Circumsphere Radius of Icosahedron given Surface to Volume Ratio evaluator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron) to evaluate the Circumsphere Radius of Icosahedron, The Circumsphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the surface to volume ratio of the Icosahedron. Circumsphere Radius of Icosahedron is denoted by r_c symbol.

How to evaluate Circumsphere Radius of Icosahedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Circumsphere 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 Circumsphere Radius of Icosahedron given Surface to Volume Ratio

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

The formula of Circumsphere Radius of Icosahedron given Surface to Volume Ratio is expressed as Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). Here is an example- 9.438064 = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*0.4).

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

With Surface to Volume Ratio of Icosahedron (R_A/V) we can find Circumsphere Radius of Icosahedron given Surface to Volume Ratio using the formula - Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). This formula also uses Square Root Function function(s).

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

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

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

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

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

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

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

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