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Insphere Radius of Icosahedron given Space Diagonal 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 \frac{2 \cdot d Space}{\sqrt{10 + (2 \cdot \sqrt{5})}}

r_i - Insphere Radius of Icosahedron?d_Space - Space Diagonal of Icosahedron?

Insphere Radius of Icosahedron given Space Diagonal Example

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

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

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

7.5492 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

7.5492m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

7.5492 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

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Insphere Radius of Icosahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

r i = 7.54921748677178m

LAST Step Rounding Answer

∴

r i = 7.5492m

Insphere Radius of Icosahedron given Space Diagonal 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

Space Diagonal of Icosahedron

The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal 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 Space Diagonal?

Insphere Radius of Icosahedron given Space Diagonal evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5))) to evaluate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Space Diagonal 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 space diagonal of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron given Space Diagonal

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

The formula of Insphere Radius of Icosahedron given Space Diagonal is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5))). Here is an example- 7.549217 = (sqrt(3)*(3+sqrt(5)))/12*(2*19)/sqrt(10+(2*sqrt(5))).

How to calculate Insphere Radius of Icosahedron given Space Diagonal?

With Space Diagonal of Icosahedron (d_Space) we can find Insphere Radius of Icosahedron given Space Diagonal using the formula - Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5))). 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 Space Diagonal be negative?

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

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

Insphere Radius of Icosahedron given Space Diagonal 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 Space Diagonal can be measured.

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