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Midsphere Radius of Dodecahedron given Surface to Volume Ratio Formula

GoMidsphere Radius of Dodecahedron Formula

GoMidsphere Radius of Dodecahedron given Volume Formula

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

r m = (3 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{R A/V \cdot (15 + (7 \cdot \sqrt{5}))}

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

Midsphere Radius of Dodecahedron given Surface to Volume Ratio Example

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

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

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

11.7557 = (3 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

11.7557m = (3 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3m⁻¹ \cdot (15 + (7 \cdot \sqrt{5}))}

11.7557 = (3 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

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Midsphere Radius of Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

r m = (3 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{R A/V \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Substitute values of Variables

∴

r m = (3 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3m⁻¹ \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Prepare to Evaluate

∴

r m = (3 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Evaluate

∴

r m = 11.7557050458495m

LAST Step Rounding Answer

∴

r m = 11.7557m

Midsphere Radius of Dodecahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the 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 Dodecahedron

Surface to Volume Ratio of Dodecahedron

The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of 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 Dodecahedron

Go Midsphere Radius of Dodecahedron

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

Go Midsphere Radius of Dodecahedron given Volume

r m = \frac{3 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Midsphere Radius of Dodecahedron given Total Surface Area

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

Go Midsphere Radius of Dodecahedron given Face Area

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

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

Midsphere Radius of Dodecahedron given Surface to Volume Ratio evaluator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))) to evaluate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron given Surface to Volume Ratio formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using surface to volume ratio of Dodecahedron. Midsphere Radius of Dodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Dodecahedron given Surface to Volume Ratio

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

The formula of Midsphere Radius of Dodecahedron given Surface to Volume Ratio is expressed as Midsphere Radius of Dodecahedron = (3+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). Here is an example- 11.75571 = (3+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5)))).

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

With Surface to Volume Ratio of Dodecahedron (R_A/V) we can find Midsphere Radius of Dodecahedron given Surface to Volume Ratio using the formula - Midsphere Radius of Dodecahedron = (3+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Midsphere Radius of Dodecahedron?

Here are the different ways to Calculate Midsphere Radius of Dodecahedron-

Midsphere Radius of Dodecahedron=(3+sqrt(5))/4*Edge Length of Dodecahedron
Midsphere Radius of Dodecahedron=(3+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Midsphere Radius of Dodecahedron=(3+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

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

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

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

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

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