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Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio Formula

GoInsphere Radius of Hexakis Octahedron Formula

GoInsphere Radius of Hexakis Octahedron given Medium Edge Formula

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Insphere Radius of Hexakis Octahedron is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere. Check FAQs

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{12 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}{R A/V \cdot (\sqrt{6 \cdot (986 + (607 \cdot \sqrt{2}))})})

r_i - Insphere Radius of Hexakis Octahedron?R_A/V - Surface to Volume Ratio of Hexakis Octahedron?

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio Example

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

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

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

15 = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{12 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}{0.2 \cdot (\sqrt{6 \cdot (986 + (607 \cdot \sqrt{2}))})})

15m = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{12 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}{0.2m⁻¹ \cdot (\sqrt{6 \cdot (986 + (607 \cdot \sqrt{2}))})})

15 = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{12 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}{0.2 \cdot (\sqrt{6 \cdot (986 + (607 \cdot \sqrt{2}))})})

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Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{12 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}{R A/V \cdot (\sqrt{6 \cdot (986 + (607 \cdot \sqrt{2}))})})

Next Step Substitute values of Variables

∴

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{12 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}{0.2m⁻¹ \cdot (\sqrt{6 \cdot (986 + (607 \cdot \sqrt{2}))})})

Next Step Prepare to Evaluate

∴

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{12 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}{0.2 \cdot (\sqrt{6 \cdot (986 + (607 \cdot \sqrt{2}))})})

LAST Step Evaluate

∴

r i = 15m

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Insphere Radius of Hexakis Octahedron

Insphere Radius of Hexakis Octahedron is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius of Hexakis Octahedron

Surface to Volume Ratio of Hexakis Octahedron

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

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 Hexakis Octahedron

Go Insphere Radius of Hexakis Octahedron

r i = (\frac{l e(Long)}{2}) \cdot (\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}})

Go Insphere Radius of Hexakis Octahedron given Medium Edge

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{14 \cdot l e(Medium)}{3 \cdot (1 + (2 \cdot \sqrt{2}))})

Go Insphere Radius of Hexakis Octahedron given Short Edge

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{14 \cdot l e(Short)}{10 - \sqrt{2}})

Go Insphere Radius of Hexakis Octahedron given Total Surface Area

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\sqrt{\frac{7 \cdot TSA}{3 \cdot \sqrt{543 + (176 \cdot \sqrt{2})}}})

How to Evaluate Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio?

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio evaluator uses Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))) to evaluate the Insphere Radius of Hexakis Octahedron, Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Hexakis Octahedron. Insphere Radius of Hexakis Octahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio

What is the formula to find Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio?

The formula of Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio is expressed as Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))). Here is an example- 15 = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(0.2*(sqrt(6*(986+(607*sqrt(2))))))).

How to calculate Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio?

With Surface to Volume Ratio of Hexakis Octahedron (R_A/V) we can find Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio using the formula - Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Insphere Radius of Hexakis Octahedron?

Here are the different ways to Calculate Insphere Radius of Hexakis Octahedron-

Insphere Radius of Hexakis Octahedron=(Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194))
Insphere Radius of Hexakis Octahedron=((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))
Insphere Radius of Hexakis Octahedron=((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))

Can the Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio be negative?

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

Which unit is used to measure Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio?

Insphere Radius of Hexakis Octahedron 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 Hexakis Octahedron given Surface to Volume Ratio can be measured.

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