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Midsphere Radius of Dodecahedron given Lateral Surface Area Formula

GoMidsphere Radius of Dodecahedron Formula

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

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

r_m - Midsphere Radius of Dodecahedron?LSA - Lateral Surface Area of Dodecahedron?

Midsphere Radius of Dodecahedron given Lateral Surface Area Example

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

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

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

13.202 = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

13.202m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

13.202 = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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Midsphere Radius of Dodecahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

r m = \frac{3 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

r m = 13.202002876147m

LAST Step Rounding Answer

∴

r m = 13.202m

Midsphere Radius of Dodecahedron given Lateral Surface Area Formula Elements

Variables

Functions

Midsphere Radius of Dodecahedron

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

Go Midsphere Radius of Dodecahedron

r m = \frac{3 + \sqrt{5}}{4} \cdot l e

Other formulas in Midsphere Radius of Dodecahedron category

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 Perimeter

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{P}{60}

Go Circumsphere Radius of Dodecahedron

r c = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{l e}{4}

Go Circumsphere Radius of Dodecahedron given Total Surface Area

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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

Midsphere Radius of Dodecahedron given Lateral Surface Area evaluator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))) to evaluate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron given Lateral Surface Area formula is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using lateral surface area of Dodecahedron. Midsphere Radius of Dodecahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Dodecahedron given Lateral Surface Area

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

The formula of Midsphere Radius of Dodecahedron given Lateral Surface Area is expressed as Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))). Here is an example- 13.202 = (3+sqrt(5))/4*sqrt((2*1750)/(5*sqrt(25+(10*sqrt(5))))).

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

With Lateral Surface Area of Dodecahedron (LSA) we can find Midsphere Radius of Dodecahedron given Lateral Surface Area using the formula - Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))). This formula also uses Square Root (sqrt) function(s).

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

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

Midsphere Radius of Dodecahedron=(3+sqrt(5))/4*Edge Length of Dodecahedron

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

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

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

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

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