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Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area Formula

GoCircumsphere Radius of Great Stellated Dodecahedron Formula

GoCircumsphere Radius of Great Stellated Dodecahedron given Ridge Length Formula

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

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

r_c - Circumradius of Great Stellated Dodecahedron?TSA - Total Surface Area of Great Stellated Dodecahedron?

Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area Example

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

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

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

22.6322 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{4600}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

22.6322m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{4600m²}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

22.6322 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{4600}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

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Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{4600m²}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \sqrt{\frac{4600}{15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

r c = 22.6322232144644m

LAST Step Rounding Answer

∴

r c = 22.6322m

Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area Formula Elements

Variables

Functions

Circumradius of Great Stellated Dodecahedron

Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Great Stellated Dodecahedron

Total Surface Area of Great Stellated Dodecahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Great Stellated 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 Circumradius of Great Stellated Dodecahedron

Go Circumsphere Radius of Great Stellated Dodecahedron

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

Go Circumsphere Radius of Great Stellated Dodecahedron given Ridge Length

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{2} \cdot \frac{1 \cdot l Ridge}{1 + \sqrt{5}}

Go Circumsphere Radius of Great Stellated Dodecahedron given Pentagram Chord

r c = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{4} \cdot \frac{l c(Pentagram)}{2 + \sqrt{5}}

Go Circumsphere Radius of Great Stellated Dodecahedron given Pyramidal Height

r c = \frac{3 \cdot h Pyramid}{2}

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

Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area evaluator uses Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5))))) to evaluate the Circumradius of Great Stellated Dodecahedron, Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area formula is defined as the radius of the sphere that contains the Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere, calculated using its total surface area. Circumradius of Great Stellated Dodecahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area

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

The formula of Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area is expressed as Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5))))). Here is an example- 22.63222 = (sqrt(3)*(3+sqrt(5)))/4*sqrt(4600/(15*sqrt(5+(2*sqrt(5))))).

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

With Total Surface Area of Great Stellated Dodecahedron (TSA) we can find Circumsphere Radius of Great Stellated Dodecahedron given Total Surface Area using the formula - Circumradius of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/4*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Great Stellated Dodecahedron?

Here are the different ways to Calculate Circumradius of Great Stellated Dodecahedron-

Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/4*Edge Length of Great Stellated Dodecahedron
Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/2*(1*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Circumradius of Great Stellated Dodecahedron=(sqrt(3)*(3+sqrt(5)))/4*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))

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

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

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

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

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