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Insphere Radius of Pentakis Dodecahedron given Leg Length Formula

GoInsphere Radius of Pentakis Dodecahedron Formula

GoInsphere Radius of Pentakis Dodecahedron given Total Surface Area Formula

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

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot l Leg}{3 \cdot (9 + \sqrt{5})})

r_i - Insphere Radius of Pentakis Dodecahedron?l_Leg - Leg Length of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron given Leg Length Example

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Here is how the Insphere Radius of Pentakis Dodecahedron given Leg Length equation looks like with Values.

Here is how the Insphere Radius of Pentakis Dodecahedron given Leg Length equation looks like with Units.

Here is how the Insphere Radius of Pentakis Dodecahedron given Leg Length equation looks like.

13.008 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot 9}{3 \cdot (9 + \sqrt{5})})

13.008m = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot 9m}{3 \cdot (9 + \sqrt{5})})

13.008 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot 9}{3 \cdot (9 + \sqrt{5})})

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Insphere Radius of Pentakis Dodecahedron given Leg Length Solution

Follow our step by step solution on how to calculate Insphere Radius of Pentakis Dodecahedron given Leg Length?

FIRST Step Consider the formula

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot l Leg}{3 \cdot (9 + \sqrt{5})})

Next Step Substitute values of Variables

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot 9m}{3 \cdot (9 + \sqrt{5})})

Next Step Prepare to Evaluate

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{38 \cdot 9}{3 \cdot (9 + \sqrt{5})})

Next Step Evaluate

∴

r i = 13.0079873308699m

LAST Step Rounding Answer

∴

r i = 13.008m

Insphere Radius of Pentakis Dodecahedron given Leg Length Formula Elements

Variables

Functions

Insphere Radius of Pentakis Dodecahedron

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius of Pentakis Dodecahedron

Leg Length of Pentakis Dodecahedron

Leg Length of Pentakis Dodecahedron is the length of the equal sides of the isosceles triangular face of Pentakis Dodecahedron.

Symbol: l_Leg

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Leg Length of Pentakis 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 Pentakis Dodecahedron

Go Insphere Radius of Pentakis Dodecahedron

r i = \frac{(3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})) \cdot l Base}{2}

Go Insphere Radius of Pentakis Dodecahedron given Total Surface Area

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\sqrt{\frac{19 \cdot TSA}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

Go Insphere Radius of Pentakis Dodecahedron given Volume

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot ({(\frac{76 \cdot V}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

Go Insphere Radius of Pentakis Dodecahedron given Midsphere Radius

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{4 \cdot r m}{3 + \sqrt{5}})

How to Evaluate Insphere Radius of Pentakis Dodecahedron given Leg Length?

Insphere Radius of Pentakis Dodecahedron given Leg Length evaluator uses Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5)))) to evaluate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Leg Length formula is defined as the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere, calculated using the leg length of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Pentakis Dodecahedron given Leg Length

What is the formula to find Insphere Radius of Pentakis Dodecahedron given Leg Length?

The formula of Insphere Radius of Pentakis Dodecahedron given Leg Length is expressed as Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5)))). Here is an example- 13.00799 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*9)/(3*(9+sqrt(5)))).

How to calculate Insphere Radius of Pentakis Dodecahedron given Leg Length?

With Leg Length of Pentakis Dodecahedron (l_Leg) we can find Insphere Radius of Pentakis Dodecahedron given Leg Length using the formula - Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5)))). This formula also uses Square Root (sqrt) function(s).

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

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

Insphere Radius of Pentakis Dodecahedron=((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2
Insphere Radius of Pentakis Dodecahedron=(3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))
Insphere Radius of Pentakis Dodecahedron=(3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))

Can the Insphere Radius of Pentakis Dodecahedron given Leg Length be negative?

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

Which unit is used to measure Insphere Radius of Pentakis Dodecahedron given Leg Length?

Insphere Radius of Pentakis Dodecahedron given Leg Length 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 Pentakis Dodecahedron given Leg Length can be measured.

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