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Circumsphere Radius of Truncated Dodecahedron given Total Surface Area Formula

GoCircumsphere Radius of Truncated Dodecahedron Formula

GoCircumsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{TSA}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

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

Circumsphere Radius of Truncated Dodecahedron given Total Surface Area Example

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

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

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

29.5485 = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{10000}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

29.5485m = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{10000m²}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

29.5485 = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{10000}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

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Circumsphere Radius of Truncated Dodecahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{TSA}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{10000m²}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{10000}{5 \cdot (\sqrt{3} + (6 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})))}}

Next Step Evaluate

∴

r c = 29.5484736839351m

LAST Step Rounding Answer

∴

r c = 29.5485m

Circumsphere Radius of Truncated Dodecahedron given Total Surface Area Formula Elements

Variables

Functions

Circumsphere Radius of Truncated Dodecahedron

Circumsphere Radius of Truncated Dodecahedron is the radius of the sphere that contains the Truncated 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 Truncated Dodecahedron

Total Surface Area of Truncated Dodecahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Truncated 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 Truncated Dodecahedron

Go Circumsphere Radius of Truncated Dodecahedron

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot l e

Go Circumsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot \frac{l e(Dodecahedron)}{\sqrt{5}}

Go Circumsphere Radius of Truncated Dodecahedron given Volume

r c = \frac{\sqrt{74 + (30 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Go Circumsphere Radius of Truncated Dodecahedron given Midsphere Radius

r c = \sqrt{74 + (30 \cdot \sqrt{5})} \cdot \frac{r m}{5 + (3 \cdot \sqrt{5})}

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

Circumsphere Radius of Truncated Dodecahedron given Total Surface Area evaluator uses Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*(sqrt(5+(2*sqrt(5)))))))) to evaluate the Circumsphere Radius of Truncated Dodecahedron, Circumsphere Radius of Truncated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using the total surface area of the Truncated Dodecahedron. Circumsphere Radius of Truncated Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Truncated Dodecahedron given Total Surface Area

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

The formula of Circumsphere Radius of Truncated Dodecahedron given Total Surface Area is expressed as Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*(sqrt(5+(2*sqrt(5)))))))). Here is an example- 29.54847 = sqrt(74+(30*sqrt(5)))/4*sqrt(10000/(5*(sqrt(3)+(6*(sqrt(5+(2*sqrt(5)))))))).

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

With Total Surface Area of Truncated Dodecahedron (TSA) we can find Circumsphere Radius of Truncated Dodecahedron given Total Surface Area using the formula - Circumsphere Radius of Truncated Dodecahedron = sqrt(74+(30*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*(sqrt(5+(2*sqrt(5)))))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumsphere Radius of Truncated Dodecahedron?

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

Circumsphere Radius of Truncated Dodecahedron=sqrt(74+(30*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
Circumsphere Radius of Truncated Dodecahedron=sqrt(74+(30*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Circumsphere Radius of Truncated Dodecahedron=sqrt(74+(30*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3)

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

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

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

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

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