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Midsphere Radius of Pentakis Dodecahedron given Volume Formula

GoMidsphere Radius of Pentakis Dodecahedron Formula

GoMidsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Formula

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Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere. Check FAQs

r m = (\frac{3 + \sqrt{5}}{4}) \cdot ({(\frac{76 \cdot V}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

r_m - Midsphere Radius of Pentakis Dodecahedron?V - Volume of Pentakis Dodecahedron?

Midsphere Radius of Pentakis Dodecahedron given Volume Example

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

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

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

13.0929 = (\frac{3 + \sqrt{5}}{4}) \cdot ({(\frac{76 \cdot 9400}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

13.0929m = (\frac{3 + \sqrt{5}}{4}) \cdot ({(\frac{76 \cdot 9400m³}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

13.0929 = (\frac{3 + \sqrt{5}}{4}) \cdot ({(\frac{76 \cdot 9400}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

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Midsphere Radius of Pentakis Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

r m = (\frac{3 + \sqrt{5}}{4}) \cdot ({(\frac{76 \cdot V}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

Next Step Substitute values of Variables

∴

r m = (\frac{3 + \sqrt{5}}{4}) \cdot ({(\frac{76 \cdot 9400m³}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

Next Step Prepare to Evaluate

∴

r m = (\frac{3 + \sqrt{5}}{4}) \cdot ({(\frac{76 \cdot 9400}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{1}{3}})

Next Step Evaluate

∴

r m = 13.0929121593898m

LAST Step Rounding Answer

∴

r m = 13.0929m

Midsphere Radius of Pentakis Dodecahedron given Volume Formula Elements

Variables

Functions

Midsphere Radius of Pentakis Dodecahedron

Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis 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 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 Midsphere Radius of Pentakis Dodecahedron

Go Midsphere Radius of Pentakis Dodecahedron

r m = (\frac{l Base}{4}) \cdot (3 + \sqrt{5})

Go Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio

r m = (\frac{3 + \sqrt{5}}{4}) \cdot (\frac{\frac{76}{19}}{R A/V}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

Go Midsphere Radius of Pentakis Dodecahedron given Leg Length

r m = (\frac{3 + \sqrt{5}}{4}) \cdot (\frac{38 \cdot l Leg}{3 \cdot (9 + \sqrt{5})})

Go Midsphere Radius of Pentakis Dodecahedron given Total Surface Area

r m = (\frac{3 + \sqrt{5}}{4}) \cdot (\sqrt{\frac{19 \cdot TSA}{15 \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})}})

How to Evaluate Midsphere Radius of Pentakis Dodecahedron given Volume?

Midsphere Radius of Pentakis Dodecahedron given Volume evaluator uses Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3)) to evaluate the Midsphere Radius of Pentakis Dodecahedron, Midsphere Radius of Pentakis Dodecahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere, calculated using the volume of the Pentakis Dodecahedron. Midsphere Radius of Pentakis Dodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Pentakis Dodecahedron given Volume

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

The formula of Midsphere Radius of Pentakis Dodecahedron given Volume is expressed as Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3)). Here is an example- 13.09291 = ((3+sqrt(5))/4)*(((76*9400)/(15*(23+(11*sqrt(5)))))^(1/3)).

How to calculate Midsphere Radius of Pentakis Dodecahedron given Volume?

With Volume of Pentakis Dodecahedron (V) we can find Midsphere Radius of Pentakis Dodecahedron given Volume using the formula - Midsphere Radius of Pentakis Dodecahedron = ((3+sqrt(5))/4)*(((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 Midsphere Radius of Pentakis Dodecahedron?

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

Midsphere Radius of Pentakis Dodecahedron=(Base Length of Pentakis Dodecahedron/4)*(3+sqrt(5))
Midsphere Radius of Pentakis Dodecahedron=((3+sqrt(5))/4)*((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5))))
Midsphere Radius of Pentakis Dodecahedron=((3+sqrt(5))/4)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))

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

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

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

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

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