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Circumsphere Radius of Icosahedron given Face Area 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 \sqrt{\frac{4 \cdot A Face}{\sqrt{3}}}

r_c - Circumsphere Radius of Icosahedron?A_Face - Face Area of Icosahedron?

Circumsphere Radius of Icosahedron given Face Area Example

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

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

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

9.6953 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

9.6953m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

9.6953 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

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Circumsphere Radius of Icosahedron given Face Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

Next Step Evaluate

∴

r c = 9.69532260321381m

LAST Step Rounding Answer

∴

r c = 9.6953m

Circumsphere Radius of Icosahedron given Face Area 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

Face Area of Icosahedron

The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area 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 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}

How to Evaluate Circumsphere Radius of Icosahedron given Face Area?

Circumsphere Radius of Icosahedron given Face Area evaluator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)) to evaluate the Circumsphere Radius of Icosahedron, The Circumsphere Radius of Icosahedron given Face Area 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 face area of the Icosahedron. Circumsphere Radius of Icosahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Icosahedron given Face Area

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

The formula of Circumsphere Radius of Icosahedron given Face Area is expressed as Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)). Here is an example- 9.695323 = sqrt(10+(2*sqrt(5)))/4*sqrt((4*45)/sqrt(3)).

How to calculate Circumsphere Radius of Icosahedron given Face Area?

With Face Area of Icosahedron (A_Face) we can find Circumsphere Radius of Icosahedron given Face Area using the formula - Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)). 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*(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 Face Area be negative?

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

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

Circumsphere Radius of Icosahedron given Face Area 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 Face Area can be measured.

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