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Insphere Radius of Pentakis Dodecahedron given Total Surface Area 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 (\sqrt{\frac{19 \cdot TSA}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

r_i - Insphere Radius of Pentakis Dodecahedron?TSA - Total Surface Area of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron given Total Surface Area Example

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

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

Here is how the Insphere Radius of Pentakis Dodecahedron given Total Surface Area equation looks like.

12.8263 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\sqrt{\frac{19 \cdot 2200}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

12.8263m = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\sqrt{\frac{19 \cdot 2200m²}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

12.8263 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\sqrt{\frac{19 \cdot 2200}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

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Insphere Radius of Pentakis Dodecahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

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})})}})

Next Step Substitute values of Variables

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\sqrt{\frac{19 \cdot 2200m²}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

Next Step Prepare to Evaluate

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\sqrt{\frac{19 \cdot 2200}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

Next Step Evaluate

∴

r i = 12.8263373475288m

LAST Step Rounding Answer

∴

r i = 12.8263m

Insphere Radius of Pentakis Dodecahedron given Total Surface Area 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

Total Surface Area of Pentakis Dodecahedron

Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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 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 Total Surface Area?

Insphere Radius of Pentakis Dodecahedron given Total Surface Area evaluator uses 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))))))) to evaluate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Total Surface Area 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 total surface area of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Pentakis Dodecahedron given Total Surface Area

What is the formula to find Insphere Radius of Pentakis Dodecahedron given Total Surface Area?

The formula of Insphere Radius of Pentakis Dodecahedron given Total Surface Area is expressed as 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))))))). Here is an example- 12.82634 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*2200)/(15*(sqrt(413+(162*sqrt(5))))))).

How to calculate Insphere Radius of Pentakis Dodecahedron given Total Surface Area?

With Total Surface Area of Pentakis Dodecahedron (TSA) we can find Insphere Radius of Pentakis Dodecahedron given Total Surface Area using the formula - 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))))))). This formula also uses Square Root Function 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))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))

Can the Insphere Radius of Pentakis Dodecahedron given Total Surface Area be negative?

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

Which unit is used to measure Insphere Radius of Pentakis Dodecahedron given Total Surface Area?

Insphere Radius of Pentakis Dodecahedron given Total Surface Area 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 Total Surface Area can be measured.

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