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Circumsphere Radius of Dodecahedron given Lateral Surface Area Formula

GoCircumsphere Radius of Dodecahedron Formula

GoCircumsphere Radius of Dodecahedron given Volume Formula

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Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere. Check FAQs

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

r_c - Circumsphere Radius of Dodecahedron?LSA - Lateral Surface Area of Dodecahedron?

Circumsphere Radius of Dodecahedron given Lateral Surface Area Example

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

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

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

14.1323 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

14.1323m = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

14.1323 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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Circumsphere Radius of Dodecahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

r c = 14.1322987663714m

LAST Step Rounding Answer

∴

r c = 14.1323m

Circumsphere Radius of Dodecahedron given Lateral Surface Area Formula Elements

Variables

Functions

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere 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 Circumsphere Radius of Dodecahedron

Go Circumsphere Radius of Dodecahedron

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

Go Circumsphere Radius of Dodecahedron given Volume

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Circumsphere Radius of Dodecahedron given Face Diagonal

r c = \frac{\sqrt{3}}{2} \cdot d Face

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 Circumsphere Radius of Dodecahedron given Lateral Surface Area?

Circumsphere Radius of Dodecahedron given Lateral Surface Area evaluator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))) to evaluate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Lateral Surface Area formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using lateral surface area of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Dodecahedron given Lateral Surface Area

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

The formula of Circumsphere Radius of Dodecahedron given Lateral Surface Area is expressed as Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))). Here is an example- 14.1323 = sqrt(3)*(1+sqrt(5))/4*sqrt((2*1750)/(5*sqrt(25+(10*sqrt(5))))).

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

With Lateral Surface Area of Dodecahedron (LSA) we can find Circumsphere Radius of Dodecahedron given Lateral Surface Area using the formula - Circumsphere Radius of Dodecahedron = sqrt(3)*(1+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 Circumsphere Radius of Dodecahedron?

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

Circumsphere Radius of Dodecahedron=sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/4
Circumsphere Radius of Dodecahedron=sqrt(3)*(1+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Circumsphere Radius of Dodecahedron=sqrt(3)/2*Face Diagonal of Dodecahedron

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

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

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

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

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