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Midsphere Radius of Icosidodecahedron given Total Surface Area Formula

GoMidsphere Radius of Icosidodecahedron Formula

GoMidsphere Radius of Icosidodecahedron given Volume 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 = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{TSA}{(5 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})}}

r_m - Midsphere Radius of Icosidodecahedron?TSA - Total Surface Area of Icosidodecahedron?

Midsphere Radius of Icosidodecahedron given Total Surface Area Example

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

Here is how the Midsphere Radius of Icosidodecahedron given Total Surface Area equation looks like.

15.3079 = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2900}{(5 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})}}

15.3079m = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2900m²}{(5 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})}}

15.3079 = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2900}{(5 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})}}

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Midsphere Radius of Icosidodecahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

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})})}}

Next Step Substitute values of Variables

∴

r m = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2900m²}{(5 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})}}

Next Step Prepare to Evaluate

∴

r m = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2900}{(5 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})}}

Next Step Evaluate

∴

r m = 15.3078718977268m

LAST Step Rounding Answer

∴

r m = 15.3079m

Midsphere Radius of Icosidodecahedron given Total Surface 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

Total Surface Area of Icosidodecahedron

Total Surface Area of Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Icosidodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface 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 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}}

Go Midsphere Radius of Icosidodecahedron given Surface to Volume Ratio

r m = \sqrt{5 + (2 \cdot \sqrt{5})} \cdot \frac{3 \cdot ((5 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}))}{R A/V \cdot (45 + (17 \cdot \sqrt{5}))}

How to Evaluate Midsphere Radius of Icosidodecahedron given Total Surface Area?

Midsphere Radius of Icosidodecahedron given Total Surface Area evaluator uses 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)))))) to evaluate the Midsphere Radius of Icosidodecahedron, Midsphere Radius of Icosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Icosidodecahedron. Midsphere Radius of Icosidodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosidodecahedron given Total Surface Area

What is the formula to find Midsphere Radius of Icosidodecahedron given Total Surface Area?

The formula of Midsphere Radius of Icosidodecahedron given Total Surface Area is expressed as 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)))))). Here is an example- 15.30787 = sqrt(5+(2*sqrt(5)))/2*sqrt(2900/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))).

How to calculate Midsphere Radius of Icosidodecahedron given Total Surface Area?

With Total Surface Area of Icosidodecahedron (TSA) we can find Midsphere Radius of Icosidodecahedron given Total Surface Area using the formula - 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)))))). This formula also uses Square Root (sqrt) 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*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)
Midsphere Radius of Icosidodecahedron=sqrt(5+(2*sqrt(5)))*Circumsphere Radius of Icosidodecahedron/(1+sqrt(5))

Can the Midsphere Radius of Icosidodecahedron given Total Surface Area be negative?

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

Which unit is used to measure Midsphere Radius of Icosidodecahedron given Total Surface Area?

Midsphere Radius of Icosidodecahedron given Total Surface 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 Total Surface Area can be measured.

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