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Midsphere Radius of Icosidodecahedron given Pentagonal Face Area Formula

GoMidsphere Radius of Icosidodecahedron Formula

GoMidsphere Radius of Icosidodecahedron given Total Surface Area Formula

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Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere. Check FAQs

r m = \sqrt{\frac{(5 + (2 \cdot \sqrt{5})) \cdot A Pentagon}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

r_m - Midsphere Radius of Icosidodecahedron?A_Pentagon - Pentagonal Face Area of Icosidodecahedron?

Midsphere Radius of Icosidodecahedron given Pentagonal Face Area Example

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Here is how the Midsphere Radius of Icosidodecahedron given Pentagonal Face Area equation looks like with Values.

Here is how the Midsphere Radius of Icosidodecahedron given Pentagonal Face Area equation looks like with Units.

Here is how the Midsphere Radius of Icosidodecahedron given Pentagonal Face Area equation looks like.

15.2966 = \sqrt{\frac{(5 + (2 \cdot \sqrt{5})) \cdot 170}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

15.2966m = \sqrt{\frac{(5 + (2 \cdot \sqrt{5})) \cdot 170m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

15.2966 = \sqrt{\frac{(5 + (2 \cdot \sqrt{5})) \cdot 170}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

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Midsphere Radius of Icosidodecahedron given Pentagonal Face Area Solution

Follow our step by step solution on how to calculate Midsphere Radius of Icosidodecahedron given Pentagonal Face Area?

FIRST Step Consider the formula

r m = \sqrt{\frac{(5 + (2 \cdot \sqrt{5})) \cdot A Pentagon}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

r m = \sqrt{\frac{(5 + (2 \cdot \sqrt{5})) \cdot 170m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

r m = \sqrt{\frac{(5 + (2 \cdot \sqrt{5})) \cdot 170}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

r m = 15.2965658394327m

LAST Step Rounding Answer

∴

r m = 15.2966m

Midsphere Radius of Icosidodecahedron given Pentagonal Face Area Formula Elements

Variables

Functions

Midsphere Radius of Icosidodecahedron

Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron 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 Icosidodecahedron

Pentagonal Face Area of Icosidodecahedron

Pentagonal Face Area of Icosidodecahedron is the total quantity of two dimensional space enclosed on any of the pentagonal faces of the Icosidodecahedron.

Symbol: A_Pentagon

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Pentagonal Face Area of Icosidodecahedron

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 Midsphere Radius of Icosidodecahedron

Go Midsphere Radius of Icosidodecahedron

r m = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot l e

Go Midsphere Radius of Icosidodecahedron given Total Surface Area

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

Go Midsphere Radius of Icosidodecahedron given Volume

r m = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{6 \cdot V}{45 + (17 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Midsphere Radius of Icosidodecahedron given Circumsphere Radius

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

How to Evaluate Midsphere Radius of Icosidodecahedron given Pentagonal Face Area?

Midsphere Radius of Icosidodecahedron given Pentagonal Face Area evaluator uses Midsphere Radius of Icosidodecahedron = sqrt(((5+(2*sqrt(5)))*Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5)))) to evaluate the Midsphere Radius of Icosidodecahedron, Midsphere Radius of Icosidodecahedron given Pentagonal Face Area formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line to that sphere, and calculated using the pentagonal face area of the Icosidodecahedron. Midsphere Radius of Icosidodecahedron is denoted by r_m symbol.

How to evaluate Midsphere Radius of Icosidodecahedron given Pentagonal Face Area using this online evaluator? To use this online evaluator for Midsphere Radius of Icosidodecahedron given Pentagonal Face Area, enter Pentagonal Face Area of Icosidodecahedron (A_Pentagon) and hit the calculate button.

FAQs on Midsphere Radius of Icosidodecahedron given Pentagonal Face Area

What is the formula to find Midsphere Radius of Icosidodecahedron given Pentagonal Face Area?

The formula of Midsphere Radius of Icosidodecahedron given Pentagonal Face Area is expressed as Midsphere Radius of Icosidodecahedron = sqrt(((5+(2*sqrt(5)))*Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5)))). Here is an example- 15.29657 = sqrt(((5+(2*sqrt(5)))*170)/sqrt(25+(10*sqrt(5)))).

How to calculate Midsphere Radius of Icosidodecahedron given Pentagonal Face Area?

With Pentagonal Face Area of Icosidodecahedron (A_Pentagon) we can find Midsphere Radius of Icosidodecahedron given Pentagonal Face Area using the formula - Midsphere Radius of Icosidodecahedron = sqrt(((5+(2*sqrt(5)))*Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5)))). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Midsphere Radius of Icosidodecahedron?

Here are the different ways to Calculate Midsphere Radius of Icosidodecahedron-

Midsphere Radius of Icosidodecahedron=sqrt(5+(2*sqrt(5)))/2*Edge Length of Icosidodecahedron
Midsphere Radius of Icosidodecahedron=sqrt(5+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Midsphere Radius of Icosidodecahedron=sqrt(5+(2*sqrt(5)))/2*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)

Can the Midsphere Radius of Icosidodecahedron given Pentagonal Face Area be negative?

No, the Midsphere Radius of Icosidodecahedron given Pentagonal Face Area, measured in Length cannot be negative.

Which unit is used to measure Midsphere Radius of Icosidodecahedron given Pentagonal Face Area?

Midsphere Radius of Icosidodecahedron given Pentagonal Face Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Midsphere Radius of Icosidodecahedron given Pentagonal Face Area can be measured.

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