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Space Diagonal of Dodecahedron given Insphere Radius Formula

GoSpace Diagonal of Dodecahedron Formula

GoSpace Diagonal of Dodecahedron given Volume Formula

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The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron. Check FAQs

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

d_Space - Space Diagonal of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Space Diagonal of Dodecahedron given Insphere Radius Example

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

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

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

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

27.685m = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

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

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Space Diagonal of Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

d Space = 27.684988592026m

LAST Step Rounding Answer

∴

d Space = 27.685m

Space Diagonal of Dodecahedron given Insphere Radius Formula Elements

Variables

Functions

Space Diagonal of Dodecahedron

The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal 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 Space Diagonal of Dodecahedron

Go Space Diagonal of Dodecahedron

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{l e}{2}

Go Space Diagonal of Dodecahedron given Volume

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Space Diagonal of Dodecahedron given Total Surface Area

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Space Diagonal of Dodecahedron given Face Area

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot A Face}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Space Diagonal of Dodecahedron given Insphere Radius?

Space Diagonal of Dodecahedron given Insphere Radius evaluator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10) to evaluate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Insphere Radius formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using insphere radius of Dodecahedron. Space Diagonal of Dodecahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Dodecahedron given Insphere Radius

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

The formula of Space Diagonal of Dodecahedron given Insphere Radius is expressed as Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10). Here is an example- 27.68499 = sqrt(3)*(1+sqrt(5))*11/sqrt((25+(11*sqrt(5)))/10).

How to calculate Space Diagonal of Dodecahedron given Insphere Radius?

With Insphere Radius of Dodecahedron (r_i) we can find Space Diagonal of Dodecahedron given Insphere Radius using the formula - Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*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 Space Diagonal of Dodecahedron?

Here are the different ways to Calculate Space Diagonal of Dodecahedron-

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

Can the Space Diagonal of Dodecahedron given Insphere Radius be negative?

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

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

Space Diagonal 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 Space Diagonal of Dodecahedron given Insphere Radius can be measured.

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