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Insphere Radius of Dodecahedron given Circumsphere Radius Formula

GoInsphere Radius of Dodecahedron Formula

GoInsphere Radius of Dodecahedron given Volume Formula

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Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere. Check FAQs

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})}

r_i - Insphere Radius of Dodecahedron?r_c - Circumsphere Radius of Dodecahedron?

Insphere Radius of Dodecahedron given Circumsphere Radius Example

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Here is how the Insphere Radius of Dodecahedron given Circumsphere Radius equation looks like with Values.

Here is how the Insphere Radius of Dodecahedron given Circumsphere Radius equation looks like with Units.

Here is how the Insphere Radius of Dodecahedron given Circumsphere Radius equation looks like.

11.1252 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})}

11.1252m = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})}

11.1252 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})}

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Insphere Radius of Dodecahedron given Circumsphere Radius Solution

Follow our step by step solution on how to calculate Insphere Radius of Dodecahedron given Circumsphere Radius?

FIRST Step Consider the formula

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Evaluate

∴

r i = 11.1251626120847m

LAST Step Rounding Answer

∴

r i = 11.1252m

Insphere Radius of Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron 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 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 Insphere Radius of Dodecahedron

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 Volume

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Insphere Radius of Dodecahedron given Total Surface Area

r i = \sqrt{\frac{TSA \cdot (25 + (11 \cdot \sqrt{5}))}{120 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Insphere Radius of Dodecahedron given Face Area

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

How to Evaluate Insphere Radius of Dodecahedron given Circumsphere Radius?

Insphere Radius of Dodecahedron given Circumsphere Radius evaluator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))) to evaluate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Circumsphere Radius formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using circumsphere radius of Dodecahedron. Insphere Radius of Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Dodecahedron given Circumsphere Radius

What is the formula to find Insphere Radius of Dodecahedron given Circumsphere Radius?

The formula of Insphere Radius of Dodecahedron given Circumsphere Radius is expressed as Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))). Here is an example- 11.12516 = sqrt((25+(11*sqrt(5)))/10)*(2*14)/(sqrt(3)*(1+sqrt(5))).

How to calculate Insphere Radius of Dodecahedron given Circumsphere Radius?

With Circumsphere Radius of Dodecahedron (r_c) we can find Insphere Radius of Dodecahedron given Circumsphere Radius using the formula - Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))). This formula also uses Square Root (sqrt) function(s).

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

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

Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Insphere Radius of Dodecahedron=sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))

Can the Insphere Radius of Dodecahedron given Circumsphere Radius be negative?

No, the Insphere Radius of Dodecahedron given Circumsphere Radius, measured in Length cannot be negative.

Which unit is used to measure Insphere Radius of Dodecahedron given Circumsphere Radius?

Insphere Radius of Dodecahedron 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 Insphere Radius of Dodecahedron given Circumsphere Radius can be measured.

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