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Space Diagonal of Dodecahedron given Midsphere 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{2 \cdot r m}{3 + \sqrt{5}}

d_Space - Space Diagonal of Dodecahedron?r_m - Midsphere Radius of Dodecahedron?

Space Diagonal of Dodecahedron given Midsphere Radius Example

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

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

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

27.8321 = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{2 \cdot 13}{3 + \sqrt{5}}

27.8321m = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{2 \cdot 13m}{3 + \sqrt{5}}

27.8321 = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{2 \cdot 13}{3 + \sqrt{5}}

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Space Diagonal of Dodecahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{2 \cdot 13m}{3 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{2 \cdot 13}{3 + \sqrt{5}}

Next Step Evaluate

∴

d Space = 27.832123002301m

LAST Step Rounding Answer

∴

d Space = 27.8321m

Space Diagonal of Dodecahedron given Midsphere 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

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the 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 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 Midsphere Radius?

Space Diagonal of Dodecahedron given Midsphere Radius evaluator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5)) to evaluate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Midsphere Radius formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using midsphere radius of Dodecahedron. Space Diagonal of Dodecahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Dodecahedron given Midsphere Radius

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

The formula of Space Diagonal of Dodecahedron given Midsphere Radius is expressed as Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5)). Here is an example- 27.83212 = sqrt(3)*(1+sqrt(5))*(2*13)/(3+sqrt(5)).

How to calculate Space Diagonal of Dodecahedron given Midsphere Radius?

With Midsphere Radius of Dodecahedron (r_m) we can find Space Diagonal of Dodecahedron given Midsphere Radius using the formula - Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5)). 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 Midsphere Radius be negative?

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

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

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

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