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Midsphere Radius of Icosahedron Formula

GoMidsphere Radius of Icosahedron given Space Diagonal Formula

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The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere. Check FAQs

r m = \frac{1 + \sqrt{5}}{4} \cdot l e

r_m - Midsphere Radius of Icosahedron?l_e - Edge Length of Icosahedron?

Midsphere Radius of Icosahedron Example

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

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

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

8.0902 = \frac{1 + \sqrt{5}}{4} \cdot 10

8.0902m = \frac{1 + \sqrt{5}}{4} \cdot 10m

8.0902 = \frac{1 + \sqrt{5}}{4} \cdot 10

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Midsphere Radius of Icosahedron Solution

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

FIRST Step Consider the formula

r m = \frac{1 + \sqrt{5}}{4} \cdot l e

Next Step Substitute values of Variables

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot 10m

Next Step Prepare to Evaluate

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot 10

Next Step Evaluate

∴

r m = 8.09016994374947m

LAST Step Rounding Answer

∴

r m = 8.0902m

Midsphere Radius of Icosahedron Formula Elements

Variables

Functions

Midsphere Radius of Icosahedron

The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere 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 Midsphere Radius of Icosahedron

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})}}

Other formulas in Midsphere Radius of Icosahedron category

Go Circumsphere Radius of Icosahedron

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

Go Insphere Radius of Icosahedron

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

How to Evaluate Midsphere Radius of Icosahedron?

Midsphere Radius of Icosahedron evaluator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron to evaluate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere. Midsphere Radius of Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosahedron

What is the formula to find Midsphere Radius of Icosahedron?

The formula of Midsphere Radius of Icosahedron is expressed as Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron. Here is an example- 8.09017 = (1+sqrt(5))/4*10.

How to calculate Midsphere Radius of Icosahedron?

With Edge Length of Icosahedron (l_e) we can find Midsphere Radius of Icosahedron using the formula - Midsphere Radius of Icosahedron = (1+sqrt(5))/4*Edge Length of Icosahedron. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Midsphere Radius of Icosahedron?

Here are the different ways to Calculate Midsphere Radius of Icosahedron-

Midsphere Radius of Icosahedron=(1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))

Can the Midsphere Radius of Icosahedron be negative?

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

Which unit is used to measure Midsphere Radius of Icosahedron?

Midsphere 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 Midsphere Radius of Icosahedron can be measured.

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