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Midsphere Radius of Icosahedron given Space Diagonal Formula

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

r_m - Midsphere Radius of Icosahedron?d_Space - Space Diagonal of Icosahedron?

Midsphere Radius of Icosahedron given Space Diagonal Example

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

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

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

8.0812 = \frac{1 + \sqrt{5}}{2} \cdot \frac{19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

8.0812m = \frac{1 + \sqrt{5}}{2} \cdot \frac{19m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

8.0812 = \frac{1 + \sqrt{5}}{2} \cdot \frac{19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

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Midsphere Radius of Icosahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

r m = \frac{1 + \sqrt{5}}{2} \cdot \frac{d Space}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

r m = \frac{1 + \sqrt{5}}{2} \cdot \frac{19m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

r m = \frac{1 + \sqrt{5}}{2} \cdot \frac{19}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

r m = 8.08118267934438m

LAST Step Rounding Answer

∴

r m = 8.0812m

Midsphere Radius of Icosahedron given Space Diagonal 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

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 Midsphere Radius of Icosahedron

Go Midsphere Radius of Icosahedron

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

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 given Space Diagonal?

Midsphere Radius of Icosahedron given Space Diagonal evaluator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5))) to evaluate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Space Diagonal formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the space diagonal of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosahedron given Space Diagonal

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

The formula of Midsphere Radius of Icosahedron given Space Diagonal is expressed as Midsphere Radius of Icosahedron = (1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5))). Here is an example- 8.081183 = (1+sqrt(5))/2*19/sqrt(10+(2*sqrt(5))).

How to calculate Midsphere Radius of Icosahedron given Space Diagonal?

With Space Diagonal of Icosahedron (d_Space) we can find Midsphere Radius of Icosahedron given Space Diagonal using the formula - Midsphere Radius of Icosahedron = (1+sqrt(5))/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 Midsphere Radius of Icosahedron?

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

Midsphere Radius of Icosahedron=(1+sqrt(5))/4*Edge Length of Icosahedron

Can the Midsphere Radius of Icosahedron given Space Diagonal be negative?

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

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

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

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