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Insphere Radius of Dodecahedron given Surface to Volume Ratio Formula

GoInsphere Radius of Dodecahedron Formula

GoInsphere Radius of Dodecahedron given Volume Formula

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

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{R A/V \cdot (15 + (7 \cdot \sqrt{5}))}

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

Insphere Radius of Dodecahedron given Surface to Volume Ratio Example

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

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

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

10 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

10m = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3m⁻¹ \cdot (15 + (7 \cdot \sqrt{5}))}

10 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

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Insphere Radius of Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{R A/V \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3m⁻¹ \cdot (15 + (7 \cdot \sqrt{5}))}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{6 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

LAST Step Evaluate

∴

r i = 10m

Insphere Radius of Dodecahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron 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 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 Insphere Radius of Dodecahedron

Go Insphere Radius of Dodecahedron

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{l e}{2}

Go Insphere Radius of Dodecahedron given Volume

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Insphere Radius of Dodecahedron given Total Surface Area

r i = \sqrt{\frac{TSA \cdot (25 + (11 \cdot \sqrt{5}))}{120 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Insphere Radius of Dodecahedron given Face Area

r i = \sqrt{\frac{A Face \cdot (25 + (11 \cdot \sqrt{5}))}{10 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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

Insphere Radius of Dodecahedron given Surface to Volume Ratio evaluator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))) to evaluate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using surface to volume ratio of Dodecahedron. Insphere Radius of Dodecahedron is denoted by r_i symbol.

How to evaluate Insphere Radius of Dodecahedron given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Insphere 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 Insphere Radius of Dodecahedron given Surface to Volume Ratio

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

The formula of Insphere Radius of Dodecahedron given Surface to Volume Ratio is expressed as Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). Here is an example- 10 = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5)))).

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

With Surface to Volume Ratio of Dodecahedron (R_A/V) we can find Insphere Radius of Dodecahedron given Surface to Volume Ratio using the formula - Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*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 Insphere Radius of Dodecahedron?

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

Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Insphere Radius of Dodecahedron=sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))

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

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

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

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

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