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Midsphere Radius of Icosahedron given Face Area Formula

GoMidsphere Radius of Icosahedron Formula

GoMidsphere Radius of Icosahedron given Circumsphere 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 = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{3}}}

r_m - Midsphere Radius of Icosahedron?A_Face - Face Area of Icosahedron?

Midsphere Radius of Icosahedron given Face Area Example

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

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

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

8.2473 = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

8.2473m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

8.2473 = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

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Midsphere Radius of Icosahedron given Face Area Solution

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

FIRST Step Consider the formula

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{3}}}

Next Step Substitute values of Variables

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 45m²}{\sqrt{3}}}

Next Step Prepare to Evaluate

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 45}{\sqrt{3}}}

Next Step Evaluate

∴

r m = 8.24733400965763m

LAST Step Rounding Answer

∴

r m = 8.2473m

Midsphere Radius of Icosahedron given Face Area 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

Face Area of Icosahedron

The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area 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 Circumsphere Radius

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

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})}}

How to Evaluate Midsphere Radius of Icosahedron given Face Area?

Midsphere Radius of Icosahedron given Face Area evaluator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)) to evaluate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Face Area 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 face area of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosahedron given Face Area

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

The formula of Midsphere Radius of Icosahedron given Face Area is expressed as Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)). Here is an example- 8.247334 = (1+sqrt(5))/4*sqrt((4*45)/sqrt(3)).

How to calculate Midsphere Radius of Icosahedron given Face Area?

With Face Area of Icosahedron (A_Face) we can find Midsphere Radius of Icosahedron given Face Area using the formula - Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3)). 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))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5))))
Midsphere Radius of Icosahedron=(1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))

Can the Midsphere Radius of Icosahedron given Face Area be negative?

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

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

Midsphere Radius of Icosahedron given Face Area 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 Face Area can be measured.

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