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Midsphere Radius of Dodecahedron Formula

GoMidsphere Radius of Dodecahedron given Lateral Surface Area 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 l e

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

Midsphere Radius of Dodecahedron Example

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

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

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

13.0902 = \frac{3 + \sqrt{5}}{4} \cdot 10

13.0902m = \frac{3 + \sqrt{5}}{4} \cdot 10m

13.0902 = \frac{3 + \sqrt{5}}{4} \cdot 10

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Midsphere Radius of Dodecahedron Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r m = \frac{3 + \sqrt{5}}{4} \cdot 10m

Next Step Prepare to Evaluate

∴

r m = \frac{3 + \sqrt{5}}{4} \cdot 10

Next Step Evaluate

∴

r m = 13.0901699437495m

LAST Step Rounding Answer

∴

r m = 13.0902m

Midsphere Radius of Dodecahedron 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

Edge Length of Dodecahedron

Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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 given Lateral Surface Area

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Other formulas in Midsphere Radius of Dodecahedron category

Go Insphere Radius of Dodecahedron

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{l e}{2}

Go Insphere Radius of Dodecahedron given Perimeter

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{P}{60}

Go Circumsphere Radius of Dodecahedron

r c = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{l e}{4}

Go Circumsphere Radius of Dodecahedron given Total Surface Area

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Midsphere Radius of Dodecahedron?

Midsphere Radius of Dodecahedron evaluator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron to evaluate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere. Midsphere Radius of Dodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Dodecahedron

What is the formula to find Midsphere Radius of Dodecahedron?

The formula of Midsphere Radius of Dodecahedron is expressed as Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron. Here is an example- 13.09017 = (3+sqrt(5))/4*10.

How to calculate Midsphere Radius of Dodecahedron?

With Edge Length of Dodecahedron (l_e) we can find Midsphere Radius of Dodecahedron using the formula - Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron. 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*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))

Can the Midsphere Radius of Dodecahedron be negative?

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

Which unit is used to measure Midsphere Radius of Dodecahedron?

Midsphere Radius of Dodecahedron 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 can be measured.

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