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Insphere Radius of Icosahedron given Face Perimeter 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 = (\sqrt{3} \cdot (3 + \sqrt{5})) \cdot \frac{P Face}{36}

r_i - Insphere Radius of Icosahedron?P_Face - Face Perimeter of Icosahedron?

Insphere Radius of Icosahedron given Face Perimeter Example

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

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

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

7.5576 = (\sqrt{3} \cdot (3 + \sqrt{5})) \cdot \frac{30}{36}

7.5576m = (\sqrt{3} \cdot (3 + \sqrt{5})) \cdot \frac{30m}{36}

7.5576 = (\sqrt{3} \cdot (3 + \sqrt{5})) \cdot \frac{30}{36}

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3D Geometry » fx Insphere Radius of Icosahedron given Face Perimeter

Insphere Radius of Icosahedron given Face Perimeter Solution

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

FIRST Step Consider the formula

r i = (\sqrt{3} \cdot (3 + \sqrt{5})) \cdot \frac{P Face}{36}

Next Step Substitute values of Variables

∴

r i = (\sqrt{3} \cdot (3 + \sqrt{5})) \cdot \frac{30m}{36}

Next Step Prepare to Evaluate

∴

r i = (\sqrt{3} \cdot (3 + \sqrt{5})) \cdot \frac{30}{36}

Next Step Evaluate

∴

r i = 7.55761314076171m

LAST Step Rounding Answer

∴

r i = 7.5576m

Insphere Radius of Icosahedron given Face Perimeter 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 Perimeter of Icosahedron

Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.

Symbol: P_Face

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Face Perimeter 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 Perimeter?

Insphere Radius of Icosahedron given Face Perimeter evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))*Face Perimeter of Icosahedron/36 to evaluate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Face Perimeter 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 perimeter of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron given Face Perimeter

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

The formula of Insphere Radius of Icosahedron given Face Perimeter is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))*Face Perimeter of Icosahedron/36. Here is an example- 7.557613 = (sqrt(3)*(3+sqrt(5)))*30/36.

How to calculate Insphere Radius of Icosahedron given Face Perimeter?

With Face Perimeter of Icosahedron (P_Face) we can find Insphere Radius of Icosahedron given Face Perimeter using the formula - Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))*Face Perimeter of Icosahedron/36. 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 Perimeter be negative?

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

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

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

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