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Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio Formula

GoMidsphere Radius of Truncated Icosahedron Formula

GoMidsphere Radius of Truncated Icosahedron given Icosahedral Edge Length Formula

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

r m = (1 + \sqrt{5}) \cdot \frac{9 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}{R A/V \cdot (125 + (43 \cdot \sqrt{5}))}

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

Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio Example

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

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

31.8735 = (1 + \sqrt{5}) \cdot \frac{9 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}{0.1 \cdot (125 + (43 \cdot \sqrt{5}))}

31.8735m = (1 + \sqrt{5}) \cdot \frac{9 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}{0.1m⁻¹ \cdot (125 + (43 \cdot \sqrt{5}))}

31.8735 = (1 + \sqrt{5}) \cdot \frac{9 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}{0.1 \cdot (125 + (43 \cdot \sqrt{5}))}

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Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

r m = (1 + \sqrt{5}) \cdot \frac{9 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}{R A/V \cdot (125 + (43 \cdot \sqrt{5}))}

Next Step Substitute values of Variables

∴

r m = (1 + \sqrt{5}) \cdot \frac{9 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}{0.1m⁻¹ \cdot (125 + (43 \cdot \sqrt{5}))}

Next Step Prepare to Evaluate

∴

r m = (1 + \sqrt{5}) \cdot \frac{9 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}{0.1 \cdot (125 + (43 \cdot \sqrt{5}))}

Next Step Evaluate

∴

r m = 31.8735282570082m

LAST Step Rounding Answer

∴

r m = 31.8735m

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

Variables

Functions

Midsphere Radius of Truncated Icosahedron

Midsphere Radius of Truncated Icosahedron is the radius of the sphere for which all the edges of the Truncated 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 Truncated Icosahedron

Surface to Volume Ratio of Truncated Icosahedron

Surface to Volume Ratio of Truncated Icosahedron is the numerical ratio of the total surface area of a Truncated Icosahedron to the volume of the Truncated Icosahedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Truncated 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 Truncated Icosahedron

Go Midsphere Radius of Truncated Icosahedron

r m = \frac{3 \cdot (1 + \sqrt{5})}{4} \cdot l e

Go Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length

r m = \frac{1 + \sqrt{5}}{4} \cdot l e(Icosahedron)

Go Midsphere Radius of Truncated Icosahedron given Total Surface Area

r m = \frac{3 \cdot (1 + \sqrt{5})}{4} \cdot \sqrt{\frac{TSA}{3 \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})}}

Go Midsphere Radius of Truncated Icosahedron given Volume

r m = \frac{3 \cdot (1 + \sqrt{5})}{4} \cdot {(\frac{4 \cdot V}{125 + (43 \cdot \sqrt{5})})}^{\frac{1}{3}}

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

Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio evaluator uses Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))*(9*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))) to evaluate the Midsphere Radius of Truncated Icosahedron, Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Truncated Icosahedron become a tangent line on that sphere, and calculated using the surface to volume ratio of the Truncated Icosahedron. Midsphere Radius of Truncated Icosahedron is denoted by r_m symbol.

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

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

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

The formula of Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio is expressed as Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))*(9*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))). Here is an example- 31.87353 = (1+sqrt(5))*(9*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(0.1*(125+(43*sqrt(5)))).

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

With Surface to Volume Ratio of Truncated Icosahedron (R_A/V) we can find Midsphere Radius of Truncated Icosahedron given Surface to Volume Ratio using the formula - Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))*(9*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))). This formula also uses Square Root (sqrt) function(s).

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

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

Midsphere Radius of Truncated Icosahedron=(3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron
Midsphere Radius of Truncated Icosahedron=(1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron
Midsphere Radius of Truncated Icosahedron=(3*(1+sqrt(5)))/4*sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))))

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

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

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

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

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