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Volume of Rotunda given Surface to Volume Ratio Formula

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Volume of Rotunda is the total quantity of three-dimensional space enclosed by the surface of the Rotunda. Check FAQs

V = \frac{1}{12} \cdot (45 + (17 \cdot \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}))})}^{3}

V - Volume of Rotunda?R_A/V - Surface to Volume Ratio of Rotunda?

Volume of Rotunda given Surface to Volume Ratio Example

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

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

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

8637.2252 = \frac{1}{12} \cdot (45 + (17 \cdot \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}))})}^{3}

8637.2252m³ = \frac{1}{12} \cdot (45 + (17 \cdot \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}))})}^{3}

8637.2252 = \frac{1}{12} \cdot (45 + (17 \cdot \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}))})}^{3}

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Volume of Rotunda given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

V = \frac{1}{12} \cdot (45 + (17 \cdot \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}))})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{1}{12} \cdot (45 + (17 \cdot \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}))})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{12} \cdot (45 + (17 \cdot \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}))})}^{3}

Next Step Evaluate

∴

V = 8637.22522398345m³

LAST Step Rounding Answer

∴

V = 8637.2252m³

Volume of Rotunda given Surface to Volume Ratio Formula Elements

Variables

Functions

Volume of Rotunda

Volume of Rotunda is the total quantity of three-dimensional space enclosed by the surface of the Rotunda.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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 Volume of Rotunda

Go Volume of Rotunda

V = \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5})) \cdot {l e}^{3}

Go Volume of Rotunda given Height

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

Go Volume of Rotunda given Total Surface Area

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

Go Volume of Rotunda given Circumsphere Radius

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

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

Volume of Rotunda given Surface to Volume Ratio evaluator uses Volume of Rotunda = 1/12*(45+(17*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)))))^3 to evaluate the Volume of Rotunda, The Volume of Rotunda given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda and is calculated using the surface to volume ratio of the Rotunda. Volume of Rotunda is denoted by V symbol.

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

FAQs on Volume of Rotunda given Surface to Volume Ratio

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

The formula of Volume of Rotunda given Surface to Volume Ratio is expressed as Volume of Rotunda = 1/12*(45+(17*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)))))^3. Here is an example- 8637.225 = 1/12*(45+(17*sqrt(5)))*((1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))/(0.3*1/12*(45+(17*sqrt(5)))))^3.

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

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

What are the other ways to Calculate Volume of Rotunda?

Here are the different ways to Calculate Volume of Rotunda-

Volume of Rotunda=1/12*(45+(17*sqrt(5)))*Edge Length of Rotunda^3
Volume of Rotunda=1/12*(45+(17*sqrt(5)))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^3
Volume of Rotunda=1/12*(45+(17*sqrt(5)))*(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))^(3/2)

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

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

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

Volume of Rotunda given Surface to Volume Ratio is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Rotunda given Surface to Volume Ratio can be measured.

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