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Circumsphere Radius of Rotunda given Surface to Volume Ratio Formula

GoCircumsphere Radius of Rotunda Formula

GoCircumsphere Radius of Rotunda given Height Formula

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Circumsphere Radius of Rotunda is the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere. Check FAQs

r c = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot (\frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{R A/V \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})

r_c - Circumsphere Radius of Rotunda?R_A/V - Surface to Volume Ratio of Rotunda?

Circumsphere Radius of Rotunda given Surface to Volume Ratio Example

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Here is how the Circumsphere Radius of Rotunda given Surface to Volume Ratio equation looks like with Values.

Here is how the Circumsphere Radius of Rotunda given Surface to Volume Ratio equation looks like with Units.

Here is how the Circumsphere Radius of Rotunda given Surface to Volume Ratio equation looks like.

17.423 = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot (\frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{0.3 \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})

17.423m = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot (\frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{0.3m⁻¹ \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})

17.423 = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot (\frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{0.3 \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})

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Circumsphere Radius of Rotunda given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Circumsphere Radius of Rotunda given Surface to Volume Ratio?

FIRST Step Consider the formula

r c = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot (\frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{R A/V \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})

Next Step Substitute values of Variables

∴

r c = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot (\frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{0.3m⁻¹ \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})

Next Step Prepare to Evaluate

∴

r c = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot (\frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{0.3 \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})

Next Step Evaluate

∴

r c = 17.4230358134644m

LAST Step Rounding Answer

∴

r c = 17.423m

Circumsphere Radius of Rotunda given Surface to Volume Ratio Formula Elements

Variables

Functions

Circumsphere Radius of Rotunda

Circumsphere Radius of Rotunda is the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Rotunda

Surface to Volume Ratio of Rotunda

Surface to Volume Ratio of Rotunda is the numerical ratio of the total surface area of a Rotunda to the volume of the Rotunda.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Rotunda

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 Rotunda

Go Circumsphere Radius of Rotunda

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

Go Circumsphere Radius of Rotunda given Height

r c = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot \frac{h}{\sqrt{1 + \frac{2}{\sqrt{5}}}}

Go Circumsphere Radius of Rotunda given Total Surface Area

r c = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot \sqrt{\frac{TSA}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

Go Circumsphere Radius of Rotunda given Volume

r c = \frac{1}{2} \cdot (1 + \sqrt{5}) \cdot {(\frac{V}{\frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})}^{\frac{1}{3}}

How to Evaluate Circumsphere Radius of Rotunda given Surface to Volume Ratio?

Circumsphere Radius of Rotunda given Surface to Volume Ratio evaluator uses Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(Surface to Volume Ratio of Rotunda*1/12*(45+(17*sqrt(5))))) to evaluate the Circumsphere Radius of Rotunda, The Circumsphere Radius of Rotunda given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere and is calculated using the surface to volume ratio of the Rotunda. Circumsphere Radius of Rotunda is denoted by r_c symbol.

How to evaluate Circumsphere Radius of Rotunda given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Circumsphere Radius of Rotunda given Surface to Volume Ratio, enter Surface to Volume Ratio of Rotunda (R_A/V) and hit the calculate button.

FAQs on Circumsphere Radius of Rotunda given Surface to Volume Ratio

What is the formula to find Circumsphere Radius of Rotunda given Surface to Volume Ratio?

The formula of Circumsphere Radius of Rotunda given Surface to Volume Ratio is expressed as Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(Surface to Volume Ratio of Rotunda*1/12*(45+(17*sqrt(5))))). Here is an example- 17.42304 = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(0.3*1/12*(45+(17*sqrt(5))))).

How to calculate Circumsphere Radius of Rotunda given Surface to Volume Ratio?

With Surface to Volume Ratio of Rotunda (R_A/V) we can find Circumsphere Radius of Rotunda given Surface to Volume Ratio using the formula - Circumsphere Radius of Rotunda = 1/2*(1+sqrt(5))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(Surface to Volume Ratio of Rotunda*1/12*(45+(17*sqrt(5))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumsphere Radius of Rotunda?

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

Circumsphere Radius of Rotunda=1/2*(1+sqrt(5))*Edge Length of Rotunda
Circumsphere Radius of Rotunda=1/2*(1+sqrt(5))*Height of Rotunda/(sqrt(1+2/sqrt(5)))
Circumsphere Radius of Rotunda=1/2*(1+sqrt(5))*sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))

Can the Circumsphere Radius of Rotunda given Surface to Volume Ratio be negative?

No, the Circumsphere Radius of Rotunda given Surface to Volume Ratio, measured in Length cannot be negative.

Which unit is used to measure Circumsphere Radius of Rotunda given Surface to Volume Ratio?

Circumsphere Radius of Rotunda given Surface to Volume Ratio 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 Rotunda given Surface to Volume Ratio can be measured.

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