FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Insphere Radius of Icosahedron Formula

GoInsphere Radius of Icosahedron given Total Surface Area Formula

Fx Copy

LaTeX Copy

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 l e

r_i - Insphere Radius of Icosahedron?l_e - Edge Length of Icosahedron?

Insphere Radius of Icosahedron Example

With values

With units

Only example

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

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

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

7.5576 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot 10

7.5576m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot 10m

7.5576 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot 10

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Insphere Radius of Icosahedron

Insphere Radius of Icosahedron Solution

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

FIRST Step Consider the formula

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot l e

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r i = 7.55761314076171m

LAST Step Rounding Answer

∴

r i = 7.5576m

Insphere Radius of Icosahedron 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

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 Insphere Radius of Icosahedron

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}}}

Other formulas in Insphere Radius of Icosahedron category

Go Circumsphere Radius of Icosahedron

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

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}}

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 Insphere Radius of Icosahedron?

Insphere Radius of Icosahedron evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron to evaluate the Insphere Radius of Icosahedron, Insphere Radius of Icosahedron 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. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron

What is the formula to find Insphere Radius of Icosahedron?

The formula of Insphere Radius of Icosahedron is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron. Here is an example- 7.557613 = (sqrt(3)*(3+sqrt(5)))/12*10.

How to calculate Insphere Radius of Icosahedron?

With Edge Length of Icosahedron (l_e) we can find Insphere Radius of Icosahedron using the formula - Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron. 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*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))

Can the Insphere Radius of Icosahedron be negative?

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

Which unit is used to measure Insphere Radius of Icosahedron?

Insphere 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 Insphere Radius of Icosahedron can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit