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Circumsphere Radius of Dodecahedron given Surface to Volume Ratio Formula

GoCircumsphere Radius of Dodecahedron Formula

GoCircumsphere Radius of Dodecahedron given Volume Formula

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Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere. Check FAQs

r c = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{R A/V \cdot (15 + (7 \cdot \sqrt{5}))}

r_c - Circumsphere Radius of Dodecahedron?R_A/V - Surface to Volume Ratio of Dodecahedron?

Circumsphere Radius of Dodecahedron given Surface to Volume Ratio Example

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

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

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

12.5841 = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

12.5841m = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3m⁻¹ \cdot (15 + (7 \cdot \sqrt{5}))}

12.5841 = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}{0.3 \cdot (15 + (7 \cdot \sqrt{5}))}

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Circumsphere Radius of Dodecahedron given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Evaluate

∴

r c = 12.5840857236482m

LAST Step Rounding Answer

∴

r c = 12.5841m

Circumsphere Radius of Dodecahedron given Surface to Volume Ratio Formula Elements

Variables

Functions

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere 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 Circumsphere Radius of Dodecahedron

Go Circumsphere Radius of Dodecahedron

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

Go Circumsphere Radius of Dodecahedron given Volume

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

Go Circumsphere Radius of Dodecahedron given Face Diagonal

r c = \frac{\sqrt{3}}{2} \cdot d Face

Go Circumsphere Radius of Dodecahedron given Total Surface Area

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

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

Circumsphere Radius of Dodecahedron given Surface to Volume Ratio evaluator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))) to evaluate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using surface to volume ratio of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

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

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

The formula of Circumsphere Radius of Dodecahedron given Surface to Volume Ratio is expressed as Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). Here is an example- 12.58409 = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5)))).

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

With Surface to Volume Ratio of Dodecahedron (R_A/V) we can find Circumsphere Radius of Dodecahedron given Surface to Volume Ratio using the formula - Circumsphere Radius of Dodecahedron = sqrt(3)*(1+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 Circumsphere Radius of Dodecahedron?

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

Circumsphere Radius of Dodecahedron=sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/4
Circumsphere Radius of Dodecahedron=sqrt(3)*(1+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Circumsphere Radius of Dodecahedron=sqrt(3)/2*Face Diagonal of Dodecahedron

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

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

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

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

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