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

r_i - Insphere Radius of Icosahedron?A_Face - Face Area of Icosahedron?

Insphere Radius of Icosahedron given Face Area Example

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

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

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

7.7044 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

7.7044m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

7.7044 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

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Insphere Radius of Icosahedron given Face Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

Next Step Evaluate

∴

r i = 7.7044314669553m

LAST Step Rounding Answer

∴

r i = 7.7044m

Insphere Radius of Icosahedron given Face Area 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

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 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 Surface to Volume Ratio

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

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})}}

How to Evaluate Insphere Radius of Icosahedron given Face Area?

Insphere Radius of Icosahedron given Face Area evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((4*Face Area of Icosahedron)/sqrt(3)) to evaluate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Face Area 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 face area of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron given Face Area

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

The formula of Insphere Radius of Icosahedron given Face Area is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((4*Face Area of Icosahedron)/sqrt(3)). Here is an example- 7.704431 = (sqrt(3)*(3+sqrt(5)))/12*sqrt((4*45)/sqrt(3)).

How to calculate Insphere Radius of Icosahedron given Face Area?

With Face Area of Icosahedron (A_Face) we can find Insphere Radius of Icosahedron given Face Area using the formula - Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((4*Face Area of Icosahedron)/sqrt(3)). 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*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

Can the Insphere Radius of Icosahedron given Face Area be negative?

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

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

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

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