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Insphere Radius of Pentakis Dodecahedron given Volume Formula

GoInsphere Radius of Pentakis Dodecahedron Formula

GoInsphere Radius of Pentakis Dodecahedron given Leg Length 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{76 \cdot V}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

r_i - Insphere Radius of Pentakis Dodecahedron?V - Volume of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron given Volume Example

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

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

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

12.8236 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot ({(\frac{76 \cdot 9400}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

12.8236m = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot ({(\frac{76 \cdot 9400m³}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

12.8236 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot ({(\frac{76 \cdot 9400}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

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Insphere Radius of Pentakis Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

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}})

Next Step Substitute values of Variables

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot ({(\frac{76 \cdot 9400m³}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

Next Step Prepare to Evaluate

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot ({(\frac{76 \cdot 9400}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

Next Step Evaluate

∴

r i = 12.8236182613616m

LAST Step Rounding Answer

∴

r i = 12.8236m

Insphere Radius of Pentakis Dodecahedron given Volume 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

Volume of Pentakis Dodecahedron

Volume of Pentakis Dodecahedron is the quantity of three dimensional space enclosed by the entire surface of Pentakis Dodecahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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 Leg Length

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})})

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 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 Volume?

Insphere Radius of Pentakis Dodecahedron given Volume evaluator uses 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)) to evaluate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Volume 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 volume of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Pentakis Dodecahedron given Volume

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

The formula of Insphere Radius of Pentakis Dodecahedron given Volume is expressed as 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)). Here is an example- 12.82362 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*9400)/(15*(23+(11*sqrt(5)))))^(1/3)).

How to calculate Insphere Radius of Pentakis Dodecahedron given Volume?

With Volume of Pentakis Dodecahedron (V) we can find Insphere Radius of Pentakis Dodecahedron given Volume using the formula - 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)). 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))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
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)))))))

Can the Insphere Radius of Pentakis Dodecahedron given Volume be negative?

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

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

Insphere Radius of Pentakis Dodecahedron given Volume 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 Volume can be measured.

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