FormulaDen.com

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

Space Diagonal of Icosahedron given Insphere Radius Formula

GoSpace Diagonal of Icosahedron given Circumsphere Radius Formula

GoSpace Diagonal of Icosahedron given Midsphere Radius Formula

Fx Copy

LaTeX Copy

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

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

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

Space Diagonal of Icosahedron given Insphere Radius Example

With values

With units

Only example

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

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

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

17.6177 = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

17.6177m = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})}

17.6177 = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

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 Space Diagonal of Icosahedron given Insphere Radius

Space Diagonal of Icosahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Substitute values of Variables

∴

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})}

Next Step Evaluate

∴

d Space = 17.6177200131075m

LAST Step Rounding Answer

∴

d Space = 17.6177m

Space Diagonal of Icosahedron given Insphere Radius Formula Elements

Variables

Functions

Space Diagonal of Icosahedron

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

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of Icosahedron

Insphere Radius of Icosahedron

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

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 Icosahedron

Go Space Diagonal of Icosahedron given Circumsphere Radius

d Space = 2 \cdot r c

Go Space Diagonal of Icosahedron given Midsphere Radius

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{2 \cdot r m}{1 + \sqrt{5}}

Go Space Diagonal of Icosahedron given Surface to Volume Ratio

d Space = \sqrt{10 + (2 \cdot \sqrt{5})} \cdot \frac{6 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot R A/V}

Go Space Diagonal of Icosahedron given Total Surface Area

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

How to Evaluate Space Diagonal of Icosahedron given Insphere Radius?

Space Diagonal of Icosahedron given Insphere Radius evaluator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))) to evaluate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the insphere radius of the Icosahedron. Space Diagonal of Icosahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Icosahedron given Insphere Radius

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

The formula of Space Diagonal of Icosahedron given Insphere Radius is expressed as Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). Here is an example- 17.61772 = sqrt(10+(2*sqrt(5)))*(6*7)/(sqrt(3)*(3+sqrt(5))).

How to calculate Space Diagonal of Icosahedron given Insphere Radius?

With Insphere Radius of Icosahedron (r_i) we can find Space Diagonal of Icosahedron given Insphere Radius using the formula - Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))*(6*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Space Diagonal of Icosahedron?

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

Space Diagonal of Icosahedron=2*Circumsphere Radius of Icosahedron
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))*(2*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))*(6*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

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

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

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

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

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit