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Insphere Radius of Icosahedron given Volume Formula

GoInsphere Radius of Icosahedron Formula

GoInsphere Radius of Icosahedron given Total Surface Area Formula

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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. Check FAQs

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

r_i - Insphere Radius of Icosahedron?V - Volume of Icosahedron?

Insphere Radius of Icosahedron given Volume Example

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

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

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

7.5787 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot {(\frac{12 \cdot 2200}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

7.5787m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot {(\frac{12 \cdot 2200m³}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

7.5787 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot {(\frac{12 \cdot 2200}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

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Insphere Radius of Icosahedron given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r i = 7.5786911044625m

LAST Step Rounding Answer

∴

r i = 7.5787m

Insphere Radius of Icosahedron given Volume Formula Elements

Variables

Functions

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

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)

Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Formula and 1100+ more formulas!

Verified by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has verified this Formula and 1500+ more formulas!

Other Formulas to find Insphere Radius of Icosahedron

Go Insphere Radius of Icosahedron

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot l e

Go Insphere Radius of Icosahedron given Total Surface Area

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}}

Go Insphere Radius of Icosahedron given Surface to Volume Ratio

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot R A/V}

Go Insphere Radius of Icosahedron given Circumsphere Radius

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}}

How to Evaluate Insphere Radius of Icosahedron given Volume?

Insphere Radius of Icosahedron given Volume evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3) to evaluate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Volume formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the volume of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron given Volume

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

The formula of Insphere Radius of Icosahedron given Volume is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3). Here is an example- 7.578691 = (sqrt(3)*(3+sqrt(5)))/12*((12*2200)/(5*(3+sqrt(5))))^(1/3).

How to calculate Insphere Radius of Icosahedron given Volume?

With Volume of Icosahedron (V) we can find Insphere Radius of Icosahedron given Volume using the formula - Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3). This formula also uses Square Root (sqrt) function(s).

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

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

Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron
Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

Can the Insphere Radius of Icosahedron given Volume be negative?

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

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

Insphere 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 Insphere Radius of Icosahedron given Volume can be measured.

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