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Midsphere Radius of Icosahedron given Total Surface Area Formula

GoMidsphere Radius of Icosahedron Formula

GoMidsphere Radius of Icosahedron given Circumsphere Radius Formula

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

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}}

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

Midsphere Radius of Icosahedron given Total Surface Area Example

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

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

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

8.1087 = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{870}{5 \cdot \sqrt{3}}}

8.1087m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{870m²}{5 \cdot \sqrt{3}}}

8.1087 = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{870}{5 \cdot \sqrt{3}}}

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Midsphere Radius of Icosahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}}

Next Step Substitute values of Variables

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{870m²}{5 \cdot \sqrt{3}}}

Next Step Prepare to Evaluate

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{870}{5 \cdot \sqrt{3}}}

Next Step Evaluate

∴

r m = 8.1087134814733m

LAST Step Rounding Answer

∴

r m = 8.1087m

Midsphere Radius of Icosahedron given Total Surface Area Formula Elements

Variables

Functions

Midsphere Radius of Icosahedron

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

Total Surface Area of Icosahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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 Midsphere Radius of Icosahedron

Go Midsphere Radius of Icosahedron

r m = \frac{1 + \sqrt{5}}{4} \cdot l e

Go Midsphere Radius of Icosahedron given Circumsphere Radius

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

Go Midsphere Radius of Icosahedron given Insphere Radius

r m = (1 + \sqrt{5}) \cdot \frac{3 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

Go Midsphere Radius of Icosahedron given Space Diagonal

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

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

Midsphere Radius of Icosahedron given Total Surface Area evaluator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))) to evaluate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the total surface area of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosahedron given Total Surface Area

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

The formula of Midsphere Radius of Icosahedron given Total Surface Area is expressed as Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))). Here is an example- 8.108713 = (1+sqrt(5))/4*sqrt(870/(5*sqrt(3))).

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

With Total Surface Area of Icosahedron (TSA) we can find Midsphere Radius of Icosahedron given Total Surface Area using the formula - Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))). This formula also uses Square Root (sqrt) function(s).

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

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

Midsphere Radius of Icosahedron=(1+sqrt(5))/4*Edge Length of Icosahedron
Midsphere Radius of Icosahedron=(1+sqrt(5))*Circumsphere Radius of Icosahedron/(sqrt(10+(2*sqrt(5))))
Midsphere Radius of Icosahedron=(1+sqrt(5))*(3*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))

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

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

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

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

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