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Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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{\frac{76}{19}}{R A/V}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

r_i - Insphere Radius of Pentakis Dodecahedron?R_A/V - Surface to Volume Ratio of Pentakis Dodecahedron?

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Example

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

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

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

15 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{\frac{76}{19}}{0.2}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

15m = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{\frac{76}{19}}{0.2m⁻¹}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

15 = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{\frac{76}{19}}{0.2}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

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Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{\frac{76}{19}}{R A/V}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

Next Step Substitute values of Variables

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{\frac{76}{19}}{0.2m⁻¹}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

Next Step Prepare to Evaluate

∴

r i = (\frac{3}{2}) \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}}) \cdot (\frac{\frac{76}{19}}{0.2}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

LAST Step Evaluate

∴

r i = 15m

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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

Surface to Volume Ratio of Pentakis Dodecahedron

Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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 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}})

How to Evaluate Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio?

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio evaluator uses Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/Surface to Volume Ratio of Pentakis Dodecahedron)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))) to evaluate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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 surface to volume ratio of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio

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

The formula of Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio is expressed as Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/Surface to Volume Ratio of Pentakis Dodecahedron)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))). Here is an example- 15 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/0.2)*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))).

How to calculate Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Pentakis Dodecahedron (R_A/V) we can find Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio using the formula - Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((76/19)/Surface to Volume Ratio of Pentakis Dodecahedron)*(sqrt((413+(162*sqrt(5))))/(23+(11*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))*((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 Surface to Volume Ratio be negative?

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

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

Insphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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 Surface to Volume Ratio can be measured.

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