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Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Formula

GoMidsphere Radius of Pentakis Dodecahedron Formula

GoMidsphere Radius of Pentakis Dodecahedron given Leg Length 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{\frac{76}{19}}{R A/V}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

r_m - Midsphere Radius of Pentakis Dodecahedron?R_A/V - Surface to Volume Ratio of Pentakis Dodecahedron?

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Example

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

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

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

15.315 = (\frac{3 + \sqrt{5}}{4}) \cdot (\frac{\frac{76}{19}}{0.2}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

15.315m = (\frac{3 + \sqrt{5}}{4}) \cdot (\frac{\frac{76}{19}}{0.2m⁻¹}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

15.315 = (\frac{3 + \sqrt{5}}{4}) \cdot (\frac{\frac{76}{19}}{0.2}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

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Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

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})})

Next Step Substitute values of Variables

∴

r m = (\frac{3 + \sqrt{5}}{4}) \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 m = (\frac{3 + \sqrt{5}}{4}) \cdot (\frac{\frac{76}{19}}{0.2}) \cdot (\frac{\sqrt{(413 + (162 \cdot \sqrt{5}))}}{23 + (11 \cdot \sqrt{5})})

Next Step Evaluate

∴

r m = 15.3149975606022m

LAST Step Rounding Answer

∴

r m = 15.315m

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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

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 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 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})})}})

Go Midsphere Radius of Pentakis Dodecahedron given Volume

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

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

Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio evaluator uses 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)))) to evaluate the Midsphere Radius of Pentakis Dodecahedron, Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio 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 surface to volume ratio of the Pentakis Dodecahedron. Midsphere Radius of Pentakis Dodecahedron is denoted by r_m symbol.

How to evaluate Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Midsphere 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 Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio

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

The formula of Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio is expressed as 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)))). Here is an example- 15.315 = ((3+sqrt(5))/4)*((76/19)/(0.2))*(sqrt((413+(162*sqrt(5))))/(23+(11*sqrt(5)))).

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

With Surface to Volume Ratio of Pentakis Dodecahedron (R_A/V) we can find Midsphere Radius of Pentakis Dodecahedron given Surface to Volume Ratio using the formula - 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)))). 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)*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
Midsphere Radius of Pentakis Dodecahedron=((3+sqrt(5))/4)*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))

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

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

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

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

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