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Midsphere Radius of Icosahedron given Circumsphere Radius Formula

GoMidsphere Radius of Icosahedron Formula

GoMidsphere Radius of Icosahedron given Insphere Radius 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 = (1 + \sqrt{5}) \cdot \frac{r c}{\sqrt{10 + (2 \cdot \sqrt{5})}}

r_m - Midsphere Radius of Icosahedron?r_c - Circumsphere Radius of Icosahedron?

Midsphere Radius of Icosahedron given Circumsphere Radius Example

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

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

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

7.6559 = (1 + \sqrt{5}) \cdot \frac{9}{\sqrt{10 + (2 \cdot \sqrt{5})}}

7.6559m = (1 + \sqrt{5}) \cdot \frac{9m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

7.6559 = (1 + \sqrt{5}) \cdot \frac{9}{\sqrt{10 + (2 \cdot \sqrt{5})}}

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Midsphere Radius of Icosahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r m = (1 + \sqrt{5}) \cdot \frac{9m}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

r m = (1 + \sqrt{5}) \cdot \frac{9}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

r m = 7.65585727516836m

LAST Step Rounding Answer

∴

r m = 7.6559m

Midsphere Radius of Icosahedron given Circumsphere Radius 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

Circumsphere Radius of Icosahedron

Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius 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

Go Midsphere Radius of Icosahedron given Insphere Radius

r m = (1 + \sqrt{5}) \cdot \frac{3 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

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})}}

Go Midsphere Radius of Icosahedron given Surface to Volume Ratio

r m = (1 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot R A/V}

How to Evaluate Midsphere Radius of Icosahedron given Circumsphere Radius?

Midsphere Radius of Icosahedron given Circumsphere Radius evaluator uses Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))) to evaluate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Circumsphere Radius 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 circumsphere radius of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosahedron given Circumsphere Radius

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

The formula of Midsphere Radius of Icosahedron given Circumsphere Radius is expressed as Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5)))). Here is an example- 7.655857 = (1+sqrt(5))*9/(sqrt(10+(2*sqrt(5)))).

How to calculate Midsphere Radius of Icosahedron given Circumsphere Radius?

With Circumsphere Radius of Icosahedron (r_c) we can find Midsphere Radius of Icosahedron given Circumsphere Radius using the formula - Midsphere Radius of Icosahedron = (1+sqrt(5))*Circumsphere Radius 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
Midsphere Radius of Icosahedron=(1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Midsphere Radius of Icosahedron=(1+sqrt(5))/2*Space Diagonal of Icosahedron/sqrt(10+(2*sqrt(5)))

Can the Midsphere Radius of Icosahedron given Circumsphere Radius be negative?

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

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

Midsphere Radius of Icosahedron given Circumsphere Radius 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 Circumsphere Radius can be measured.

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