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Circumsphere Radius of Dodecahedron given Total Surface Area Formula

GoCircumsphere Radius of Dodecahedron 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{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

r_c - Circumsphere Radius of Dodecahedron?TSA - Total Surface Area of Dodecahedron?

Circumsphere Radius of Dodecahedron given Total Surface Area Example

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

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

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

14.1323 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

14.1323m = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2100m²}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

14.1323 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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Circumsphere Radius of Dodecahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

r c = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{TSA}{3 \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{2100m²}{3 \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{2100}{3 \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 Total 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

Total Surface Area of Dodecahedron

Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total 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}

Other formulas in Circumsphere 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 Midsphere Radius of Dodecahedron

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

Go Midsphere Radius of Dodecahedron given Lateral Surface Area

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

How to Evaluate Circumsphere Radius of Dodecahedron given Total Surface Area?

Circumsphere Radius of Dodecahedron given Total Surface Area evaluator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))) to evaluate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Total 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 total surface area of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Dodecahedron given Total Surface Area

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

The formula of Circumsphere Radius of Dodecahedron given Total Surface Area is expressed as Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))). Here is an example- 14.1323 = sqrt(3)*(1+sqrt(5))/4*sqrt(2100/(3*sqrt(25+(10*sqrt(5))))).

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

With Total Surface Area of Dodecahedron (TSA) we can find Circumsphere Radius of Dodecahedron given Total Surface Area using the formula - Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*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

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

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

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

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

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