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Circumsphere Radius of Icosahedron given Insphere Radius Formula

GoCircumsphere Radius of Icosahedron Formula

GoCircumsphere Radius of Icosahedron given Midsphere 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 r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

r_c - Circumsphere Radius of Icosahedron?r_i - Insphere Radius of Icosahedron?

Circumsphere Radius of Icosahedron given Insphere Radius Example

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Here is how the Circumsphere Radius of Icosahedron given Insphere Radius equation looks like with Values.

Here is how the Circumsphere Radius of Icosahedron given Insphere Radius equation looks like with Units.

Here is how the Circumsphere Radius of Icosahedron given Insphere Radius equation looks like.

8.8089 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

8.8089m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})}

8.8089 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

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Circumsphere Radius of Icosahedron given Insphere Radius Solution

Follow our step by step solution on how to calculate Circumsphere Radius of Icosahedron given Insphere Radius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Evaluate

∴

r c = 8.80886000655373m

LAST Step Rounding Answer

∴

r c = 8.8089m

Circumsphere Radius of Icosahedron given Insphere Radius 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

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 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 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 Surface to Volume Ratio

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

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 Insphere Radius?

Circumsphere Radius of Icosahedron given Insphere Radius evaluator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to evaluate the Circumsphere Radius of Icosahedron, The Circumsphere Radius of Icosahedron given Insphere Radius 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 insphere radius of the Icosahedron. Circumsphere Radius of Icosahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Icosahedron given Insphere Radius

What is the formula to find Circumsphere Radius of Icosahedron given Insphere Radius?

The formula of Circumsphere Radius of Icosahedron given Insphere Radius is expressed as Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). Here is an example- 8.80886 = sqrt(10+(2*sqrt(5)))/4*(12*7)/(sqrt(3)*(3+sqrt(5))).

How to calculate Circumsphere Radius of Icosahedron given Insphere Radius?

With Insphere Radius of Icosahedron (r_i) we can find Circumsphere Radius of Icosahedron given Insphere Radius using the formula - Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(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 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*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Circumsphere Radius of Icosahedron=sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

Can the Circumsphere Radius of Icosahedron given Insphere Radius be negative?

No, the Circumsphere Radius of Icosahedron given Insphere Radius, measured in Length cannot be negative.

Which unit is used to measure Circumsphere Radius of Icosahedron given Insphere Radius?

Circumsphere Radius of Icosahedron given Insphere Radius 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 Insphere Radius can be measured.

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