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Circumsphere Radius of Great Dodecahedron given Volume Formula

GoCircumsphere Radius of Great Dodecahedron Formula

GoCircumsphere Radius of Great Dodecahedron given Ridge Length Formula

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

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot V}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

r_c - Circumsphere Radius of Great Dodecahedron?V - Volume of Great Dodecahedron?

Circumsphere Radius of Great Dodecahedron given Volume Example

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Here is how the Circumsphere Radius of Great Dodecahedron given Volume equation looks like with Values.

Here is how the Circumsphere Radius of Great Dodecahedron given Volume equation looks like with Units.

Here is how the Circumsphere Radius of Great Dodecahedron given Volume equation looks like.

9.5206 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot 1550}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

9.5206m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot 1550m³}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

9.5206 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot 1550}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

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Circumsphere Radius of Great Dodecahedron given Volume Solution

Follow our step by step solution on how to calculate Circumsphere Radius of Great Dodecahedron given Volume?

FIRST Step Consider the formula

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot V}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot 1550m³}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{4 \cdot 1550}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

Next Step Evaluate

∴

r c = 9.52063908928949m

LAST Step Rounding Answer

∴

r c = 9.5206m

Circumsphere Radius of Great Dodecahedron given Volume Formula Elements

Variables

Functions

Circumsphere Radius of Great Dodecahedron

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

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Great Dodecahedron

Volume of Great Dodecahedron

Volume of Great Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Great Dodecahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Great 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 Great Dodecahedron

Go Circumsphere Radius of Great Dodecahedron

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot l e

Go Circumsphere Radius of Great Dodecahedron given Ridge Length

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{2 \cdot l Ridge}{\sqrt{5} - 1}

Go Circumsphere Radius of Great Dodecahedron given Pyramidal Height

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 - \sqrt{5})}

Go Circumsphere Radius of Great Dodecahedron given Total Surface Area

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

How to Evaluate Circumsphere Radius of Great Dodecahedron given Volume?

Circumsphere Radius of Great Dodecahedron given Volume evaluator uses Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3) to evaluate the Circumsphere Radius of Great Dodecahedron, Circumsphere Radius of Great Dodecahedron given Volume formula is defined as the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere, calculated using its volume. Circumsphere Radius of Great Dodecahedron is denoted by r_c symbol.

How to evaluate Circumsphere Radius of Great Dodecahedron given Volume using this online evaluator? To use this online evaluator for Circumsphere Radius of Great Dodecahedron given Volume, enter Volume of Great Dodecahedron (V) and hit the calculate button.

FAQs on Circumsphere Radius of Great Dodecahedron given Volume

What is the formula to find Circumsphere Radius of Great Dodecahedron given Volume?

The formula of Circumsphere Radius of Great Dodecahedron given Volume is expressed as Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3). Here is an example- 9.520639 = sqrt(10+(2*sqrt(5)))/4*((4*1550)/(5*(sqrt(5)-1)))^(1/3).

How to calculate Circumsphere Radius of Great Dodecahedron given Volume?

With Volume of Great Dodecahedron (V) we can find Circumsphere Radius of Great Dodecahedron given Volume using the formula - Circumsphere Radius of Great Dodecahedron = sqrt(10+(2*sqrt(5)))/4*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3). This formula also uses Square Root (sqrt) function(s).

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

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

Circumsphere Radius of Great Dodecahedron=sqrt(10+(2*sqrt(5)))/4*Edge Length of Great Dodecahedron
Circumsphere Radius of Great Dodecahedron=sqrt(10+(2*sqrt(5)))/4*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)
Circumsphere Radius of Great Dodecahedron=sqrt(10+(2*sqrt(5)))/4*(6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))

Can the Circumsphere Radius of Great Dodecahedron given Volume be negative?

No, the Circumsphere Radius of Great Dodecahedron given Volume, measured in Length cannot be negative.

Which unit is used to measure Circumsphere Radius of Great Dodecahedron given Volume?

Circumsphere Radius of Great Dodecahedron given Volume 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 Dodecahedron given Volume can be measured.

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