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Midsphere Radius of Dodecahedron given Space Diagonal 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}}{2} \cdot \frac{d Space}{\sqrt{3} \cdot (1 + \sqrt{5})}

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

Midsphere Radius of Dodecahedron given Space Diagonal Example

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

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

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

13.0784 = \frac{3 + \sqrt{5}}{2} \cdot \frac{28}{\sqrt{3} \cdot (1 + \sqrt{5})}

13.0784m = \frac{3 + \sqrt{5}}{2} \cdot \frac{28m}{\sqrt{3} \cdot (1 + \sqrt{5})}

13.0784 = \frac{3 + \sqrt{5}}{2} \cdot \frac{28}{\sqrt{3} \cdot (1 + \sqrt{5})}

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Midsphere Radius of Dodecahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

r m = \frac{3 + \sqrt{5}}{2} \cdot \frac{d Space}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Substitute values of Variables

∴

r m = \frac{3 + \sqrt{5}}{2} \cdot \frac{28m}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

r m = \frac{3 + \sqrt{5}}{2} \cdot \frac{28}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Evaluate

∴

r m = 13.078413025478m

LAST Step Rounding Answer

∴

r m = 13.0784m

Midsphere Radius of Dodecahedron given Space Diagonal 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

Space Diagonal of Dodecahedron

The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal 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 Area

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

How to Evaluate Midsphere Radius of Dodecahedron given Space Diagonal?

Midsphere Radius of Dodecahedron given Space Diagonal evaluator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))) to evaluate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron given Space Diagonal 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 space diagonal of Dodecahedron. Midsphere Radius of Dodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Dodecahedron given Space Diagonal

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

The formula of Midsphere Radius of Dodecahedron given Space Diagonal is expressed as Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))). Here is an example- 13.07841 = (3+sqrt(5))/2*28/(sqrt(3)*(1+sqrt(5))).

How to calculate Midsphere Radius of Dodecahedron given Space Diagonal?

With Space Diagonal of Dodecahedron (d_Space) we can find Midsphere Radius of Dodecahedron given Space Diagonal using the formula - Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+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 Space Diagonal be negative?

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

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

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

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