FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Circumsphere Radius of Dodecahedron given Insphere Radius Formula

GoCircumsphere Radius of Dodecahedron Formula

GoCircumsphere Radius of Dodecahedron given Volume Formula

Fx Copy

LaTeX Copy

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 \frac{1 + \sqrt{5}}{2} \cdot \frac{r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

r_c - Circumsphere Radius of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Circumsphere Radius of Dodecahedron given Insphere Radius Example

With values

With units

Only example

Here is how the Circumsphere Radius of Dodecahedron given Insphere Radius equation looks like with Values.

Here is how the Circumsphere Radius of Dodecahedron given Insphere Radius equation looks like with Units.

Here is how the Circumsphere Radius of Dodecahedron given Insphere Radius equation looks like.

13.8425 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \frac{11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

13.8425m = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \frac{11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

13.8425 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \frac{11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Circumsphere Radius of Dodecahedron given Insphere Radius

Circumsphere Radius of Dodecahedron given Insphere Radius Solution

Follow our step by step solution on how to calculate Circumsphere Radius of Dodecahedron given Insphere Radius?

FIRST Step Consider the formula

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \frac{r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Next Step Substitute values of Variables

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \frac{11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Next Step Prepare to Evaluate

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \frac{11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Next Step Evaluate

∴

r c = 13.842494296013m

LAST Step Rounding Answer

∴

r c = 13.8425m

Circumsphere Radius of Dodecahedron given Insphere Radius 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

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

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 Insphere Radius?

Circumsphere Radius of Dodecahedron given Insphere Radius evaluator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10) to evaluate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Insphere Radius 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 insphere radius of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

How to evaluate Circumsphere Radius of Dodecahedron given Insphere Radius using this online evaluator? To use this online evaluator for Circumsphere Radius of Dodecahedron given Insphere Radius, enter Insphere Radius of Dodecahedron (r_i) and hit the calculate button.

FAQs on Circumsphere Radius of Dodecahedron given Insphere Radius

What is the formula to find Circumsphere Radius of Dodecahedron given Insphere Radius?

The formula of Circumsphere Radius of Dodecahedron given Insphere Radius is expressed as Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10). Here is an example- 13.84249 = sqrt(3)*(1+sqrt(5))/2*11/sqrt((25+(11*sqrt(5)))/10).

How to calculate Circumsphere Radius of Dodecahedron given Insphere Radius?

With Insphere Radius of Dodecahedron (r_i) we can find Circumsphere Radius of Dodecahedron given Insphere Radius using the formula - Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10). 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 Insphere Radius be negative?

No, the Circumsphere Radius of Dodecahedron given Insphere Radius, measured in Length cannot be negative.

Which unit is used to measure Circumsphere Radius of Dodecahedron given Insphere Radius?

Circumsphere Radius of Dodecahedron given Insphere Radius 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 Insphere Radius can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit