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Insphere Radius of Hexakis Octahedron given Midsphere Radius 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{4 \cdot r m}{1 + (2 \cdot \sqrt{2})})

r_i - Insphere Radius of Hexakis Octahedron?r_m - Midsphere Radius of Hexakis Octahedron?

Insphere Radius of Hexakis Octahedron given Midsphere Radius Example

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Here is how the Insphere Radius of Hexakis Octahedron given Midsphere Radius equation looks like with Values.

Here is how the Insphere Radius of Hexakis Octahedron given Midsphere Radius equation looks like with Units.

Here is how the Insphere Radius of Hexakis Octahedron given Midsphere Radius equation looks like.

18.5526 = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{4 \cdot 19}{1 + (2 \cdot \sqrt{2})})

18.5526m = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{4 \cdot 19m}{1 + (2 \cdot \sqrt{2})})

18.5526 = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{4 \cdot 19}{1 + (2 \cdot \sqrt{2})})

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Insphere Radius of Hexakis Octahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{4 \cdot r m}{1 + (2 \cdot \sqrt{2})})

Next Step Substitute values of Variables

∴

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{4 \cdot 19m}{1 + (2 \cdot \sqrt{2})})

Next Step Prepare to Evaluate

∴

r i = (\frac{\sqrt{\frac{402 + (195 \cdot \sqrt{2})}{194}}}{2}) \cdot (\frac{4 \cdot 19}{1 + (2 \cdot \sqrt{2})})

Next Step Evaluate

∴

r i = 18.5525685486838m

LAST Step Rounding Answer

∴

r i = 18.5526m

Insphere Radius of Hexakis Octahedron given Midsphere Radius 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

Midsphere Radius of Hexakis Octahedron

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

Insphere Radius of Hexakis Octahedron given Midsphere Radius evaluator uses Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2)))) to evaluate the Insphere Radius of Hexakis Octahedron, Insphere Radius of Hexakis Octahedron given Midsphere Radius 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 the midsphere radius of Hexakis Octahedron. Insphere Radius of Hexakis Octahedron is denoted by r_i symbol.

How to evaluate Insphere Radius of Hexakis Octahedron given Midsphere Radius using this online evaluator? To use this online evaluator for Insphere Radius of Hexakis Octahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Octahedron (r_m) and hit the calculate button.

FAQs on Insphere Radius of Hexakis Octahedron given Midsphere Radius

What is the formula to find Insphere Radius of Hexakis Octahedron given Midsphere Radius?

The formula of Insphere Radius of Hexakis Octahedron given Midsphere Radius is expressed as Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2)))). Here is an example- 18.55257 = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*19)/(1+(2*sqrt(2)))).

How to calculate Insphere Radius of Hexakis Octahedron given Midsphere Radius?

With Midsphere Radius of Hexakis Octahedron (r_m) we can find Insphere Radius of Hexakis Octahedron given Midsphere Radius using the formula - Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*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 Midsphere Radius be negative?

No, the Insphere Radius of Hexakis Octahedron given Midsphere Radius, measured in Length cannot be negative.

Which unit is used to measure Insphere Radius of Hexakis Octahedron given Midsphere Radius?

Insphere Radius of Hexakis Octahedron given Midsphere Radius 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 Midsphere Radius can be measured.

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