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Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio Formula

GoMidsphere Radius of Truncated Dodecahedron Formula

GoMidsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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

r m = (5 + (3 \cdot \sqrt{5})) \cdot \frac{3 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{R A/V \cdot (99 + (47 \cdot \sqrt{5}))}

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

Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio Example

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

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

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

34.7609 = (5 + (3 \cdot \sqrt{5})) \cdot \frac{3 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1 \cdot (99 + (47 \cdot \sqrt{5}))}

34.7609m = (5 + (3 \cdot \sqrt{5})) \cdot \frac{3 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1m⁻¹ \cdot (99 + (47 \cdot \sqrt{5}))}

34.7609 = (5 + (3 \cdot \sqrt{5})) \cdot \frac{3 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1 \cdot (99 + (47 \cdot \sqrt{5}))}

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Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

r m = (5 + (3 \cdot \sqrt{5})) \cdot \frac{3 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{R A/V \cdot (99 + (47 \cdot \sqrt{5}))}

Next Step Substitute values of Variables

∴

r m = (5 + (3 \cdot \sqrt{5})) \cdot \frac{3 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1m⁻¹ \cdot (99 + (47 \cdot \sqrt{5}))}

Next Step Prepare to Evaluate

∴

r m = (5 + (3 \cdot \sqrt{5})) \cdot \frac{3 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}{0.1 \cdot (99 + (47 \cdot \sqrt{5}))}

Next Step Evaluate

∴

r m = 34.7608501661344m

LAST Step Rounding Answer

∴

r m = 34.7609m

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

Variables

Functions

Midsphere Radius of Truncated Dodecahedron

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

Surface to Volume Ratio of Truncated Dodecahedron

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

Go Midsphere Radius of Truncated Dodecahedron

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

Go Midsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length

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

Go Midsphere Radius of Truncated Dodecahedron given Total Surface Area

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot \sqrt{\frac{TSA}{5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}}

Go Midsphere Radius of Truncated Dodecahedron given Volume

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

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

Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio evaluator uses Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))) to evaluate the Midsphere Radius of Truncated Dodecahedron, Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the surface to volume ratio of the Truncated Dodecahedron. Midsphere Radius of Truncated Dodecahedron is denoted by r_m symbol.

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

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

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

The formula of Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio is expressed as Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))). Here is an example- 34.76085 = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(0.1*(99+(47*sqrt(5)))).

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

With Surface to Volume Ratio of Truncated Dodecahedron (R_A/V) we can find Midsphere Radius of Truncated Dodecahedron given Surface to Volume Ratio using the formula - Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))*(3*(sqrt(3)+(6*sqrt(5+(2*sqrt(5))))))/(Surface to Volume Ratio of Truncated Dodecahedron*(99+(47*sqrt(5)))). This formula also uses Square Root (sqrt) function(s).

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

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

Midsphere Radius of Truncated Dodecahedron=(5+(3*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
Midsphere Radius of Truncated Dodecahedron=(5+(3*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Midsphere Radius of Truncated Dodecahedron=(5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))

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

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

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

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

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