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Volume of Rotunda given Circumsphere Radius 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{2 \cdot r c}{1 + \sqrt{5}})}^{3}

V - Volume of Rotunda?r_c - Circumsphere Radius of Rotunda?

Volume of Rotunda given Circumsphere Radius Example

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

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

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

6689.0232 = \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{3}

6689.0232m³ = \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{3}

6689.0232 = \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{3}

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Volume of Rotunda given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{3}

Next Step Evaluate

∴

V = 6689.02323285254m³

LAST Step Rounding Answer

∴

V = 6689.0232m³

Volume of Rotunda given Circumsphere Radius 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

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

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 Surface to Volume Ratio

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}

How to Evaluate Volume of Rotunda given Circumsphere Radius?

Volume of Rotunda given Circumsphere Radius evaluator uses Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^3 to evaluate the Volume of Rotunda, The Volume of Rotunda given Circumsphere Radius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda and is calculated using the circumsphere radius of the Rotunda. Volume of Rotunda is denoted by V symbol.

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

FAQs on Volume of Rotunda given Circumsphere Radius

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

The formula of Volume of Rotunda given Circumsphere Radius is expressed as Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^3. Here is an example- 6689.023 = 1/12*(45+(17*sqrt(5)))*((2*16)/(1+sqrt(5)))^3.

How to calculate Volume of Rotunda given Circumsphere Radius?

With Circumsphere Radius of Rotunda (r_c) we can find Volume of Rotunda given Circumsphere Radius using the formula - Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+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 Circumsphere Radius be negative?

No, the Volume of Rotunda given Circumsphere Radius, measured in Volume cannot be negative.

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

Volume of Rotunda given Circumsphere Radius 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 Circumsphere Radius can be measured.

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