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Volume of Solid of Revolution given Surface to Volume Ratio Formula

GoVolume of Solid of Revolution Formula

GoVolume of Solid of Revolution given Lateral Surface Area Formula

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Volume of Solid of Revolution is the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution. Check FAQs

V = (2 \cdot π \cdot r Area Centroid) \cdot (\frac{LSA + (({(r Top + r Bottom)}^{2}) \cdot π)}{2 \cdot π \cdot r Area Centroid \cdot R A/V})

V - Volume of Solid of Revolution?r_{Area Centroid} - Radius at Area Centroid of Solid of Revolution?LSA - Lateral Surface Area of Solid of Revolution?r_Top - Top Radius of Solid of Revolution?r_Bottom - Bottom Radius of Solid of Revolution?R_A/V - Surface to Volume Ratio of Solid of Revolution?π - Archimedes' constant?

Volume of Solid of Revolution given Surface to Volume Ratio Example

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

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

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

3990.3334 = (2 \cdot 3.1416 \cdot 12) \cdot (\frac{2360 + (({(10 + 20)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 12 \cdot 1.3})

3990.3334m³ = (2 \cdot 3.1416 \cdot 12m) \cdot (\frac{2360m² + (({(10m + 20m)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 12m \cdot 1.3m⁻¹})

3990.3334 = (2 \cdot 3.1416 \cdot 12) \cdot (\frac{2360 + (({(10 + 20)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 12 \cdot 1.3})

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Volume of Solid of Revolution given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

V = (2 \cdot π \cdot r Area Centroid) \cdot (\frac{LSA + (({(r Top + r Bottom)}^{2}) \cdot π)}{2 \cdot π \cdot r Area Centroid \cdot R A/V})

Next Step Substitute values of Variables

∴

V = (2 \cdot π \cdot 12m) \cdot (\frac{2360m² + (({(10m + 20m)}^{2}) \cdot π)}{2 \cdot π \cdot 12m \cdot 1.3m⁻¹})

Next Step Substitute values of Constants

∴

V = (2 \cdot 3.1416 \cdot 12m) \cdot (\frac{2360m² + (({(10m + 20m)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 12m \cdot 1.3m⁻¹})

Next Step Prepare to Evaluate

∴

V = (2 \cdot 3.1416 \cdot 12) \cdot (\frac{2360 + (({(10 + 20)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 12 \cdot 1.3})

Next Step Evaluate

∴

V = 3990.33337556216m³

LAST Step Rounding Answer

∴

V = 3990.3334m³

Volume of Solid of Revolution given Surface to Volume Ratio Formula Elements

Variables

Constants

Volume of Solid of Revolution

Volume of Solid of Revolution is the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Solid of Revolution

Radius at Area Centroid of Solid of Revolution

Radius at Area Centroid of Solid of Revolution is the horizontal distance from the centroidal point with respect to area under the revolving curve to the axis of rotation of the Solid of Revolution.

Symbol: r_{Area Centroid}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius at Area Centroid of Solid of Revolution

Lateral Surface Area of Solid of Revolution

Lateral Surface Area of Solid of Revolution is the total quantity of two dimensional space enclosed on the lateral surface of the Solid of Revolution.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of Solid of Revolution

Top Radius of Solid of Revolution

Top Radius of Solid of Revolution is the horizontal distance from the top end point of the revolving curve to the axis of rotation of the Solid of Revolution.

Symbol: r_Top

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Radius of Solid of Revolution

Bottom Radius of Solid of Revolution

Bottom Radius of Solid of Revolution is the horizontal distance from the bottom end point of the revolving curve to the axis of rotation of the Solid of Revolution.

Symbol: r_Bottom

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Bottom Radius of Solid of Revolution

Surface to Volume Ratio of Solid of Revolution

Surface to Volume Ratio of Solid of Revolution is defined as the fraction of surface area to volume of Solid of Revolution.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Solid of Revolution

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Volume of Solid of Revolution

Go Volume of Solid of Revolution

V = 2 \cdot π \cdot A Curve \cdot r Area Centroid

Go Volume of Solid of Revolution given Lateral Surface Area

V = (2 \cdot π \cdot A Curve) \cdot (\frac{LSA + (({(r Top + r Bottom)}^{2}) \cdot π)}{2 \cdot π \cdot A Curve \cdot R A/V})

How to Evaluate Volume of Solid of Revolution given Surface to Volume Ratio?

Volume of Solid of Revolution given Surface to Volume Ratio evaluator uses Volume of Solid of Revolution = (2*pi*Radius at Area Centroid of Solid of Revolution)*((Lateral Surface Area of Solid of Revolution+(((Top Radius of Solid of Revolution+Bottom Radius of Solid of Revolution)^2)*pi))/(2*pi*Radius at Area Centroid of Solid of Revolution*Surface to Volume Ratio of Solid of Revolution)) to evaluate the Volume of Solid of Revolution, Volume of Solid of Revolution given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution , calculated using its surface to volume ratio. Volume of Solid of Revolution is denoted by V symbol.

How to evaluate Volume of Solid of Revolution given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Volume of Solid of Revolution given Surface to Volume Ratio, enter Radius at Area Centroid of Solid of Revolution (r_{Area Centroid}), Lateral Surface Area of Solid of Revolution (LSA), Top Radius of Solid of Revolution (r_Top), Bottom Radius of Solid of Revolution (r_Bottom) & Surface to Volume Ratio of Solid of Revolution (R_A/V) and hit the calculate button.

FAQs on Volume of Solid of Revolution given Surface to Volume Ratio

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

The formula of Volume of Solid of Revolution given Surface to Volume Ratio is expressed as Volume of Solid of Revolution = (2*pi*Radius at Area Centroid of Solid of Revolution)*((Lateral Surface Area of Solid of Revolution+(((Top Radius of Solid of Revolution+Bottom Radius of Solid of Revolution)^2)*pi))/(2*pi*Radius at Area Centroid of Solid of Revolution*Surface to Volume Ratio of Solid of Revolution)). Here is an example- 3990.333 = (2*pi*12)*((2360+(((10+20)^2)*pi))/(2*pi*12*1.3)).

How to calculate Volume of Solid of Revolution given Surface to Volume Ratio?

With Radius at Area Centroid of Solid of Revolution (r_{Area Centroid}), Lateral Surface Area of Solid of Revolution (LSA), Top Radius of Solid of Revolution (r_Top), Bottom Radius of Solid of Revolution (r_Bottom) & Surface to Volume Ratio of Solid of Revolution (R_A/V) we can find Volume of Solid of Revolution given Surface to Volume Ratio using the formula - Volume of Solid of Revolution = (2*pi*Radius at Area Centroid of Solid of Revolution)*((Lateral Surface Area of Solid of Revolution+(((Top Radius of Solid of Revolution+Bottom Radius of Solid of Revolution)^2)*pi))/(2*pi*Radius at Area Centroid of Solid of Revolution*Surface to Volume Ratio of Solid of Revolution)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Volume of Solid of Revolution?

Here are the different ways to Calculate Volume of Solid of Revolution-

Volume of Solid of Revolution=2*pi*Area under Curve Solid of Revolution*Radius at Area Centroid of Solid of Revolution
Volume of Solid of Revolution=(2*pi*Area under Curve Solid of Revolution)*((Lateral Surface Area of Solid of Revolution+(((Top Radius of Solid of Revolution+Bottom Radius of Solid of Revolution)^2)*pi))/(2*pi*Area under Curve Solid of Revolution*Surface to Volume Ratio of Solid of Revolution))

Can the Volume of Solid of Revolution given Surface to Volume Ratio be negative?

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

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

Volume of Solid of Revolution 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 Solid of Revolution given Surface to Volume Ratio can be measured.

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Volume of Solid of Revolution given Surface to Volume Ratio Formula

​GoVolume of Solid of Revolution Formula

​GoVolume of Solid of Revolution given Lateral Surface Area Formula

Volume of Solid of Revolution given Surface to Volume Ratio Example

Volume of Solid of Revolution given Surface to Volume Ratio Solution

Volume of Solid of Revolution given Surface to Volume Ratio Formula Elements

Other Formulas to find Volume of Solid of Revolution

How to Evaluate Volume of Solid of Revolution given Surface to Volume Ratio?

FAQs on Volume of Solid of Revolution given Surface to Volume Ratio

Variable Name

GoVolume of Solid of Revolution Formula

GoVolume of Solid of Revolution given Lateral Surface Area Formula