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Insphere Radius of Dodecahedron given Midsphere 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 m}{3 + \sqrt{5}}

r_i - Insphere Radius of Dodecahedron?r_m - Midsphere Radius of Dodecahedron?

Insphere Radius of Dodecahedron given Midsphere Radius Example

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

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

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

11.0585 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 13}{3 + \sqrt{5}}

11.0585m = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 13m}{3 + \sqrt{5}}

11.0585 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 13}{3 + \sqrt{5}}

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Insphere Radius of Dodecahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 13m}{3 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{2 \cdot 13}{3 + \sqrt{5}}

Next Step Evaluate

∴

r i = 11.0584605085765m

LAST Step Rounding Answer

∴

r i = 11.0585m

Insphere Radius of Dodecahedron given Midsphere 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

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

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 Midsphere Radius?

Insphere Radius of Dodecahedron given Midsphere Radius evaluator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5)) to evaluate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Midsphere 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 midsphere radius of Dodecahedron. Insphere Radius of Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Dodecahedron given Midsphere Radius

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

The formula of Insphere Radius of Dodecahedron given Midsphere Radius is expressed as Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5)). Here is an example- 11.05846 = sqrt((25+(11*sqrt(5)))/10)*(2*13)/(3+sqrt(5)).

How to calculate Insphere Radius of Dodecahedron given Midsphere Radius?

With Midsphere Radius of Dodecahedron (r_m) we can find Insphere Radius of Dodecahedron given Midsphere Radius using the formula - Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Midsphere Radius of Dodecahedron)/(3+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 Midsphere Radius be negative?

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

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

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

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