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Circumsphere Radius of Icosahedron Formula

GoCircumsphere Radius of Icosahedron given Volume 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 l e

r_c - Circumsphere Radius of Icosahedron?l_e - Edge Length of Icosahedron?

Circumsphere Radius of Icosahedron Example

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

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

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

9.5106 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot 10

9.5106m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot 10m

9.5106 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot 10

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Circumsphere Radius of Icosahedron Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r c = 9.51056516295153m

LAST Step Rounding Answer

∴

r c = 9.5106m

Circumsphere Radius of Icosahedron 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

Edge Length of Icosahedron

Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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 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}}

Other formulas in Circumsphere Radius of Icosahedron category

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 Midsphere Radius of Icosahedron

r m = \frac{1 + \sqrt{5}}{4} \cdot l e

Go Midsphere Radius of Icosahedron given Space Diagonal

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

How to Evaluate Circumsphere Radius of Icosahedron?

Circumsphere Radius of Icosahedron evaluator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron to evaluate the Circumsphere Radius of Icosahedron, Circumsphere Radius of Icosahedron 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. Circumsphere Radius of Icosahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Icosahedron

What is the formula to find Circumsphere Radius of Icosahedron?

The formula of Circumsphere Radius of Icosahedron is expressed as Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron. Here is an example- 9.510565 = sqrt(10+(2*sqrt(5)))/4*10.

How to calculate Circumsphere Radius of Icosahedron?

With Edge Length of Icosahedron (l_e) we can find Circumsphere Radius of Icosahedron using the formula - Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length 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*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)

Can the Circumsphere Radius of Icosahedron be negative?

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

Which unit is used to measure Circumsphere Radius of Icosahedron?

Circumsphere Radius of Icosahedron 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 can be measured.

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