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Midsphere Radius of Dodecahedron given Face Area Formula

GoMidsphere Radius of Dodecahedron Formula

GoMidsphere Radius of Dodecahedron given Volume Formula

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

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

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

Midsphere Radius of Dodecahedron given Face Area Example

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

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

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

13.202 = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

13.202m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

13.202 = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

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Midsphere Radius of Dodecahedron given Face Area Solution

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

FIRST Step Consider the formula

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

r m = 13.202002876147m

LAST Step Rounding Answer

∴

r m = 13.202m

Midsphere Radius of Dodecahedron given Face Area Formula Elements

Variables

Functions

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron 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 Dodecahedron

Face Area of Dodecahedron

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

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area of Dodecahedron

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 Dodecahedron

Go Midsphere Radius of Dodecahedron

r m = \frac{3 + \sqrt{5}}{4} \cdot l e

Go Midsphere Radius of Dodecahedron given Volume

r m = \frac{3 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Midsphere Radius of Dodecahedron given Total Surface Area

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Midsphere Radius of Dodecahedron given Face Diagonal

r m = \frac{3 + \sqrt{5}}{2} \cdot \frac{d Face}{1 + \sqrt{5}}

How to Evaluate Midsphere Radius of Dodecahedron given Face Area?

Midsphere Radius of Dodecahedron given Face Area evaluator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5)))) to evaluate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron given Face Area formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using face area of Dodecahedron. Midsphere Radius of Dodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Dodecahedron given Face Area

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

The formula of Midsphere Radius of Dodecahedron given Face Area is expressed as Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5)))). Here is an example- 13.202 = (3+sqrt(5))/4*sqrt((4*175)/sqrt(25+(10*sqrt(5)))).

How to calculate Midsphere Radius of Dodecahedron given Face Area?

With Face Area of Dodecahedron (A_Face) we can find Midsphere Radius of Dodecahedron given Face Area using the formula - Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5)))). This formula also uses Square Root (sqrt) function(s).

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

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

Midsphere Radius of Dodecahedron=(3+sqrt(5))/4*Edge Length of Dodecahedron
Midsphere Radius of Dodecahedron=(3+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Midsphere Radius of Dodecahedron=(3+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

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

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

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

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

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