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Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Formula

GoMidsphere Radius of Hexakis Icosahedron given Short Edge Formula

GoMidsphere Radius of Hexakis Icosahedron given Truncated Icosidodecahedron Edge Formula

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Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere. Check FAQs

r m = \frac{1}{8} \cdot (\frac{6}{5} \cdot \frac{\sqrt{10 \cdot (417 + 107 \cdot \sqrt{5})}}{R A/V \cdot \sqrt{6 \cdot (185 + 82 \cdot \sqrt{5})}}) \cdot (5 + 3 \cdot \sqrt{5})

r_m - Midsphere Radius of Hexakis Icosahedron?R_A/V - Surface to Volume Ratio of Hexakis Icosahedron?

Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Example

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

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

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

15.1314 = \frac{1}{8} \cdot (\frac{6}{5} \cdot \frac{\sqrt{10 \cdot (417 + 107 \cdot \sqrt{5})}}{0.2 \cdot \sqrt{6 \cdot (185 + 82 \cdot \sqrt{5})}}) \cdot (5 + 3 \cdot \sqrt{5})

15.1314m = \frac{1}{8} \cdot (\frac{6}{5} \cdot \frac{\sqrt{10 \cdot (417 + 107 \cdot \sqrt{5})}}{0.2m⁻¹ \cdot \sqrt{6 \cdot (185 + 82 \cdot \sqrt{5})}}) \cdot (5 + 3 \cdot \sqrt{5})

15.1314 = \frac{1}{8} \cdot (\frac{6}{5} \cdot \frac{\sqrt{10 \cdot (417 + 107 \cdot \sqrt{5})}}{0.2 \cdot \sqrt{6 \cdot (185 + 82 \cdot \sqrt{5})}}) \cdot (5 + 3 \cdot \sqrt{5})

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Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

r m = \frac{1}{8} \cdot (\frac{6}{5} \cdot \frac{\sqrt{10 \cdot (417 + 107 \cdot \sqrt{5})}}{R A/V \cdot \sqrt{6 \cdot (185 + 82 \cdot \sqrt{5})}}) \cdot (5 + 3 \cdot \sqrt{5})

Next Step Substitute values of Variables

∴

r m = \frac{1}{8} \cdot (\frac{6}{5} \cdot \frac{\sqrt{10 \cdot (417 + 107 \cdot \sqrt{5})}}{0.2m⁻¹ \cdot \sqrt{6 \cdot (185 + 82 \cdot \sqrt{5})}}) \cdot (5 + 3 \cdot \sqrt{5})

Next Step Prepare to Evaluate

∴

r m = \frac{1}{8} \cdot (\frac{6}{5} \cdot \frac{\sqrt{10 \cdot (417 + 107 \cdot \sqrt{5})}}{0.2 \cdot \sqrt{6 \cdot (185 + 82 \cdot \sqrt{5})}}) \cdot (5 + 3 \cdot \sqrt{5})

Next Step Evaluate

∴

r m = 15.1313905619247m

LAST Step Rounding Answer

∴

r m = 15.1314m

Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Midsphere Radius of Hexakis Icosahedron

Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron 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 Hexakis Icosahedron

Surface to Volume Ratio of Hexakis Icosahedron

Surface to Volume Ratio of Hexakis Icosahedron is what part of or fraction of total volume of Hexakis Icosahedron 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 Hexakis Icosahedron

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 Hexakis Icosahedron

Go Midsphere Radius of Hexakis Icosahedron given Short Edge

r m = (\frac{5 + (3 \cdot \sqrt{5})}{8}) \cdot (\frac{44 \cdot l e(Short)}{5 \cdot (7 - \sqrt{5})})

Go Midsphere Radius of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

r m = (\frac{5 + (3 \cdot \sqrt{5})}{8}) \cdot (\frac{2}{5}) \cdot (l e(Truncated Icosidodecahedron)) \cdot (\sqrt{15 \cdot (5 - \sqrt{5})})

Go Midsphere Radius of Hexakis Icosahedron given Medium Edge

r m = (\frac{5 + (3 \cdot \sqrt{5})}{8}) \cdot (\frac{22 \cdot l e(Medium)}{3 \cdot (4 + \sqrt{5})})

Go Midsphere Radius of Hexakis Icosahedron

r m = \frac{l e(Long)}{8} \cdot (5 + 3 \cdot \sqrt{5})

How to Evaluate Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?

Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio evaluator uses Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)) to evaluate the Midsphere Radius of Hexakis Icosahedron, The Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere, calculated using the surface to volume ratio of Hexakis Icosahedron. Midsphere Radius of Hexakis Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio

What is the formula to find Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?

The formula of Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio is expressed as Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)). Here is an example- 15.13139 = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(0.2*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)).

How to calculate Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Hexakis Icosahedron (R_A/V) we can find Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio using the formula - Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Midsphere Radius of Hexakis Icosahedron?

Here are the different ways to Calculate Midsphere Radius of Hexakis Icosahedron-

Midsphere Radius of Hexakis Icosahedron=((5+(3*sqrt(5)))/8)*((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))
Midsphere Radius of Hexakis Icosahedron=((5+(3*sqrt(5)))/8)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))
Midsphere Radius of Hexakis Icosahedron=((5+(3*sqrt(5)))/8)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))

Can the Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio be negative?

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

Which unit is used to measure Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?

Midsphere Radius of Hexakis Icosahedron 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 Hexakis Icosahedron given Surface to Volume Ratio can be measured.

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