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Insphere Radius of Dodecahedron given Volume Formula

GoInsphere Radius of Dodecahedron Formula

GoInsphere Radius of Dodecahedron given Total Surface Area Formula

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Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere. Check FAQs

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

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

Insphere Radius of Dodecahedron given Volume Example

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

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

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

11.153 = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

11.153m = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

11.153 = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

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Insphere Radius of Dodecahedron given Volume Solution

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

FIRST Step Consider the formula

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot 7700m³}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot 7700}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Next Step Evaluate

∴

r i = 11.1529988246622m

LAST Step Rounding Answer

∴

r i = 11.153m

Insphere Radius of Dodecahedron given Volume Formula Elements

Variables

Functions

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron 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 Dodecahedron

Volume of Dodecahedron

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Dodecahedron

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 Insphere Radius of Dodecahedron

Go Insphere Radius of Dodecahedron

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{l e}{2}

Go Insphere Radius of Dodecahedron given Total Surface Area

r i = \sqrt{\frac{TSA \cdot (25 + (11 \cdot \sqrt{5}))}{120 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Insphere Radius of Dodecahedron given Face Area

r i = \sqrt{\frac{A Face \cdot (25 + (11 \cdot \sqrt{5}))}{10 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Insphere Radius of Dodecahedron given Face Perimeter

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{P Face}{10}

How to Evaluate Insphere Radius of Dodecahedron given Volume?

Insphere Radius of Dodecahedron given Volume evaluator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3) to evaluate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Volume formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using volume of Dodecahedron. Insphere Radius of Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Dodecahedron given Volume

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

The formula of Insphere Radius of Dodecahedron given Volume is expressed as Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). Here is an example- 11.153 = sqrt((25+(11*sqrt(5)))/10)/2*((4*7700)/(15+(7*sqrt(5))))^(1/3).

How to calculate Insphere Radius of Dodecahedron given Volume?

With Volume of Dodecahedron (V) we can find Insphere Radius of Dodecahedron given Volume using the formula - Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). This formula also uses Square Root (sqrt) function(s).

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

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

Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
Insphere Radius of Dodecahedron=sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))
Insphere Radius of Dodecahedron=sqrt((Face Area of Dodecahedron*(25+(11*sqrt(5))))/(10*sqrt(25+(10*sqrt(5)))))

Can the Insphere Radius of Dodecahedron given Volume be negative?

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

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

Insphere Radius of Dodecahedron 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 Dodecahedron given Volume can be measured.

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