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Area under Curve Solid of Revolution is defined as the total quantity of two dimensional space enclosed under the curve in a plane, which revolve around a fixed axis to form the Solid of Revolution. Check FAQs
ACurve=LSA+(((rTop+rBottom)2)⋅π)2⋅π⋅rArea Centroid⋅RA/V
ACurve - Area under Curve Solid of Revolution?LSA - Lateral Surface Area of Solid of Revolution?rTop - Top Radius of Solid of Revolution?rBottom - Bottom Radius of Solid of Revolution?rArea Centroid - Radius at Area Centroid of Solid of Revolution?RA/V - Surface to Volume Ratio of Solid of Revolution?π - Archimedes' constant?

Area under Curve of Solid of Revolution Example

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Here is how the Area under Curve of Solid of Revolution equation looks like with Values.

Here is how the Area under Curve of Solid of Revolution equation looks like with Units.

Here is how the Area under Curve of Solid of Revolution equation looks like.

52.9234Edit=2360Edit+(((10Edit+20Edit)2)⋅3.1416)2⋅3.1416⋅12Edit⋅1.3Edit
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Area under Curve of Solid of Revolution Solution

Follow our step by step solution on how to calculate Area under Curve of Solid of Revolution?

FIRST Step Consider the formula
ACurve=LSA+(((rTop+rBottom)2)⋅π)2⋅π⋅rArea Centroid⋅RA/V
Next Step Substitute values of Variables
∴ ACurve=2360m²+(((10m+20m)2)⋅π)2⋅π⋅12m⋅1.3m⁻¹
Next Step Substitute values of Constants
∴ ACurve=2360m²+(((10m+20m)2)⋅3.1416)2⋅3.1416⋅12m⋅1.3m⁻¹
Next Step Prepare to Evaluate
∴ ACurve=2360+(((10+20)2)⋅3.1416)2⋅3.1416⋅12⋅1.3
Next Step Evaluate
∴ACurve=52.9234401087739m²
LAST Step Rounding Answer
∴ACurve=52.9234m²

Area under Curve of Solid of Revolution Formula Elements

Variables
Constants
Area under Curve Solid of Revolution
Area under Curve Solid of Revolution is defined as the total quantity of two dimensional space enclosed under the curve in a plane, which revolve around a fixed axis to form the Solid of Revolution.
Symbol: ACurve
Measurement: AreaUnit: m²
Note: Value should be greater than 0.
Formulas to find Area under Curve Solid of RevolutionOpen Variable
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 RevolutionOpen Variable
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: rTop
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Top Radius of Solid of RevolutionOpen Variable
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: rBottom
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Bottom Radius of Solid of RevolutionOpen Variable
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: rArea Centroid
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Radius at Area Centroid of Solid of RevolutionOpen Variable
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: RA/V
Measurement: Reciprocal LengthUnit: m⁻¹
Note: Value should be greater than 0.
Formulas to find Surface to Volume Ratio of Solid of RevolutionOpen Variable
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 Area under Curve Solid of Revolution

​Go Area under Curve of Solid of Revolution given Volume
ACurve=V2⋅π⋅rArea Centroid

How to Evaluate Area under Curve of Solid of Revolution?

Area under Curve of Solid of Revolution evaluator uses 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*Radius at Area Centroid of Solid of Revolution*Surface to Volume Ratio of Solid of Revolution) to evaluate the Area under Curve Solid of Revolution, Area under Curve of Solid of Revolution formula is defined as the total quantity of two dimensional space enclosed under the curve in a plane, which revolve around a fixed axis to form the Solid of Revolution. Area under Curve Solid of Revolution is denoted by ACurve symbol.

How to evaluate Area under Curve of Solid of Revolution using this online evaluator? To use this online evaluator for Area under Curve of Solid of Revolution, enter Lateral Surface Area of Solid of Revolution (LSA), Top Radius of Solid of Revolution (rTop), Bottom Radius of Solid of Revolution (rBottom), Radius at Area Centroid of Solid of Revolution (rArea Centroid) & Surface to Volume Ratio of Solid of Revolution (RA/V) and hit the calculate button.

FAQs on Area under Curve of Solid of Revolution

What is the formula to find Area under Curve of Solid of Revolution?
The formula of Area under Curve of Solid of Revolution is expressed as 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*Radius at Area Centroid of Solid of Revolution*Surface to Volume Ratio of Solid of Revolution). Here is an example- 52.92344 = (2360+(((10+20)^2)*pi))/(2*pi*12*1.3).
How to calculate Area under Curve of Solid of Revolution?
With Lateral Surface Area of Solid of Revolution (LSA), Top Radius of Solid of Revolution (rTop), Bottom Radius of Solid of Revolution (rBottom), Radius at Area Centroid of Solid of Revolution (rArea Centroid) & Surface to Volume Ratio of Solid of Revolution (RA/V) we can find Area under Curve of Solid of Revolution using the formula - 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*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 Area under Curve Solid of Revolution?
Here are the different ways to Calculate Area under Curve Solid of Revolution-
  • Area under Curve Solid of Revolution=Volume of Solid of Revolution/(2*pi*Radius at Area Centroid of Solid of Revolution)OpenImg
Can the Area under Curve of Solid of Revolution be negative?
No, the Area under Curve of Solid of Revolution, measured in Area cannot be negative.
Which unit is used to measure Area under Curve of Solid of Revolution?
Area under Curve of Solid of Revolution is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area under Curve of Solid of Revolution can be measured.
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