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Insphere Radius of Dodecahedron given Lateral Surface Area Formula

GoInsphere Radius of Dodecahedron Formula

GoInsphere Radius of Dodecahedron given Volume 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 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{\sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}}{2}

r_i - Insphere Radius of Dodecahedron?LSA - Lateral Surface Area of Dodecahedron?

Insphere Radius of Dodecahedron given Lateral Surface Area Example

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Here is how the Insphere Radius of Dodecahedron given Lateral Surface Area equation looks like with Values.

Here is how the Insphere Radius of Dodecahedron given Lateral Surface Area equation looks like with Units.

Here is how the Insphere Radius of Dodecahedron given Lateral Surface Area equation looks like.

11.2303 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{\sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}}{2}

11.2303m = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{\sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}}{2}

11.2303 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{\sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}}{2}

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Insphere Radius of Dodecahedron given Lateral Surface Area Solution

Follow our step by step solution on how to calculate Insphere Radius of Dodecahedron given Lateral Surface Area?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{\sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}}{2}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{\sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}}{2}

Next Step Evaluate

∴

r i = 11.2302944184604m

LAST Step Rounding Answer

∴

r i = 11.2303m

Insphere Radius of Dodecahedron given Lateral Surface Area 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

Lateral Surface Area of Dodecahedron

Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area 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 Volume

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}}

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})}}}

How to Evaluate Insphere Radius of Dodecahedron given Lateral Surface Area?

Insphere Radius of Dodecahedron given Lateral Surface Area evaluator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2 to evaluate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Lateral Surface Area 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 lateral surface area of Dodecahedron. Insphere Radius of Dodecahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Dodecahedron given Lateral Surface Area

What is the formula to find Insphere Radius of Dodecahedron given Lateral Surface Area?

The formula of Insphere Radius of Dodecahedron given Lateral Surface Area is expressed as Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2. Here is an example- 11.23029 = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*1750)/(5*sqrt(25+(10*sqrt(5)))))/2.

How to calculate Insphere Radius of Dodecahedron given Lateral Surface Area?

With Lateral Surface Area of Dodecahedron (LSA) we can find Insphere Radius of Dodecahedron given Lateral Surface Area using the formula - Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2. 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((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Insphere Radius of Dodecahedron=sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))

Can the Insphere Radius of Dodecahedron given Lateral Surface Area be negative?

No, the Insphere Radius of Dodecahedron given Lateral Surface Area, measured in Length cannot be negative.

Which unit is used to measure Insphere Radius of Dodecahedron given Lateral Surface Area?

Insphere Radius of Dodecahedron given Lateral Surface Area 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 Lateral Surface Area can be measured.

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