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Midsphere Radius of Icosahedron given Volume 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 {(\frac{\frac{12}{5} \cdot V}{3 + \sqrt{5}})}^{\frac{1}{3}}

r_m - Midsphere Radius of Icosahedron?V - Volume of Icosahedron?

Midsphere Radius of Icosahedron given Volume Example

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Here is how the Midsphere Radius of Icosahedron given Volume equation looks like with Values.

Here is how the Midsphere Radius of Icosahedron given Volume equation looks like with Units.

Here is how the Midsphere Radius of Icosahedron given Volume equation looks like.

8.1127 = \frac{1 + \sqrt{5}}{4} \cdot {(\frac{\frac{12}{5} \cdot 2200}{3 + \sqrt{5}})}^{\frac{1}{3}}

8.1127m = \frac{1 + \sqrt{5}}{4} \cdot {(\frac{\frac{12}{5} \cdot 2200m³}{3 + \sqrt{5}})}^{\frac{1}{3}}

8.1127 = \frac{1 + \sqrt{5}}{4} \cdot {(\frac{\frac{12}{5} \cdot 2200}{3 + \sqrt{5}})}^{\frac{1}{3}}

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Midsphere Radius of Icosahedron given Volume Solution

Follow our step by step solution on how to calculate Midsphere Radius of Icosahedron given Volume?

FIRST Step Consider the formula

r m = \frac{1 + \sqrt{5}}{4} \cdot {(\frac{\frac{12}{5} \cdot V}{3 + \sqrt{5}})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot {(\frac{\frac{12}{5} \cdot 2200m³}{3 + \sqrt{5}})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot {(\frac{\frac{12}{5} \cdot 2200}{3 + \sqrt{5}})}^{\frac{1}{3}}

Next Step Evaluate

∴

r m = 8.1127331929171m

LAST Step Rounding Answer

∴

r m = 8.1127m

Midsphere Radius of Icosahedron given Volume 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

Volume of Icosahedron

Volume of Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Icosahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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 Volume?

Midsphere Radius of Icosahedron given Volume evaluator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3) to evaluate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Volume 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 volume of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosahedron given Volume

What is the formula to find Midsphere Radius of Icosahedron given Volume?

The formula of Midsphere Radius of Icosahedron given Volume is expressed as Midsphere Radius of Icosahedron = (1+sqrt(5))/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3). Here is an example- 8.112733 = (1+sqrt(5))/4*((12/5*2200)/(3+sqrt(5)))^(1/3).

How to calculate Midsphere Radius of Icosahedron given Volume?

With Volume of Icosahedron (V) we can find Midsphere Radius of Icosahedron given Volume using the formula - Midsphere Radius of Icosahedron = (1+sqrt(5))/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3). This formula also uses Square Root Function 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 Volume be negative?

No, the Midsphere Radius of Icosahedron given Volume, measured in Length cannot be negative.

Which unit is used to measure Midsphere Radius of Icosahedron given Volume?

Midsphere Radius of Icosahedron given Volume 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 Volume can be measured.

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