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Area under curve of Solid of Revolution Solution

STEP 0: Pre-Calculation Summary
Formula Used
area_under_curve = (Lateral Surface Area 1+(((Top Radius+Bottom Radius)^2)*pi))/(2*pi*Radius at area centroid*Surface to Volume Ratio)
ACurve = (SALateral_1+(((rTop+rBottom)^2)*pi))/(2*pi*rAreaCentroid*RAV)
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Lateral Surface Area 1 - Lateral Surface Area 1 is the area of the lateral surface of any shape or object. (Measured in Square Meter)
Top Radius - Top Radius is the radius measured at top of object or shape. (Measured in Meter)
Bottom Radius - Bottom Radius is the radius measured at bottom of any shape or object. (Measured in Meter)
Radius at area centroid - Radius at area centroid is the radius measured at area centroid. (Measured in Meter)
Surface to Volume Ratio - Surface to Volume Ratio is fraction of surface to volume. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
Lateral Surface Area 1: 817 Square Meter --> 817 Square Meter No Conversion Required
Top Radius: 3 Meter --> 3 Meter No Conversion Required
Bottom Radius: 1 Meter --> 1 Meter No Conversion Required
Radius at area centroid: 5 Meter --> 5 Meter No Conversion Required
Surface to Volume Ratio: 0.5 Hundred --> 0.5 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ACurve = (SALateral_1+(((rTop+rBottom)^2)*pi))/(2*pi*rAreaCentroid*RAV) --> (817+(((3+1)^2)*pi))/(2*pi*5*0.5)
Evaluating ... ...
ACurve = 55.2118354024314
STEP 3: Convert Result to Output's Unit
55.2118354024314 Square Meter --> No Conversion Required
FINAL ANSWER
55.2118354024314 Square Meter <-- Area under curve
(Calculation completed in 00.016 seconds)

3 Area under curve and Curve length of Solid of Revolution Calculators

Area under curve of Solid of Revolution
area_under_curve = (Lateral Surface Area 1+(((Top Radius+Bottom Radius)^2)*pi))/(2*pi*Radius at area centroid*Surface to Volume Ratio) Go
Curve length of Solid of Revolution
curve_length_1 = (Lateral Surface Area 1/2*pi*Radius at curve centroid) Go
Area under curve of Solid of Revolution given volume
area_under_curve = Volume Polyhedron/(2*pi*Radius at area centroid) Go

Area under curve of Solid of Revolution Formula

area_under_curve = (Lateral Surface Area 1+(((Top Radius+Bottom Radius)^2)*pi))/(2*pi*Radius at area centroid*Surface to Volume Ratio)
ACurve = (SALateral_1+(((rTop+rBottom)^2)*pi))/(2*pi*rAreaCentroid*RAV)

What is Solid of Revolution?

In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane.

How to Calculate Area under curve of Solid of Revolution?

Area under curve of Solid of Revolution calculator uses area_under_curve = (Lateral Surface Area 1+(((Top Radius+Bottom Radius)^2)*pi))/(2*pi*Radius at area centroid*Surface to Volume Ratio) to calculate the Area under curve, Area under curve of Solid of Revolution formula is defined as definite integral of a curve. Area under curve and is denoted by ACurve symbol.

How to calculate Area under curve of Solid of Revolution using this online calculator? To use this online calculator for Area under curve of Solid of Revolution, enter Lateral Surface Area 1 (SALateral_1), Top Radius (rTop), Bottom Radius (rBottom), Radius at area centroid (rAreaCentroid) & Surface to Volume Ratio (RAV) and hit the calculate button. Here is how the Area under curve of Solid of Revolution calculation can be explained with given input values -> 55.21184 = (817+(((3+1)^2)*pi))/(2*pi*5*0.5).

FAQ

What is Area under curve of Solid of Revolution?
Area under curve of Solid of Revolution formula is defined as definite integral of a curve and is represented as ACurve = (SALateral_1+(((rTop+rBottom)^2)*pi))/(2*pi*rAreaCentroid*RAV) or area_under_curve = (Lateral Surface Area 1+(((Top Radius+Bottom Radius)^2)*pi))/(2*pi*Radius at area centroid*Surface to Volume Ratio). Lateral Surface Area 1 is the area of the lateral surface of any shape or object, Top Radius is the radius measured at top of object or shape, Bottom Radius is the radius measured at bottom of any shape or object, Radius at area centroid is the radius measured at area centroid & Surface to Volume Ratio is fraction of surface to volume.
How to calculate Area under curve of Solid of Revolution?
Area under curve of Solid of Revolution formula is defined as definite integral of a curve is calculated using area_under_curve = (Lateral Surface Area 1+(((Top Radius+Bottom Radius)^2)*pi))/(2*pi*Radius at area centroid*Surface to Volume Ratio). To calculate Area under curve of Solid of Revolution, you need Lateral Surface Area 1 (SALateral_1), Top Radius (rTop), Bottom Radius (rBottom), Radius at area centroid (rAreaCentroid) & Surface to Volume Ratio (RAV). With our tool, you need to enter the respective value for Lateral Surface Area 1, Top Radius, Bottom Radius, Radius at area centroid & Surface to Volume Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Area under curve?
In this formula, Area under curve uses Lateral Surface Area 1, Top Radius, Bottom Radius, Radius at area centroid & Surface to Volume Ratio. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • area_under_curve = Volume Polyhedron/(2*pi*Radius at area centroid)
  • area_under_curve = (Lateral Surface Area 1+(((Top Radius+Bottom Radius)^2)*pi))/(2*pi*Radius at area centroid*Surface to Volume Ratio)
  • curve_length_1 = (Lateral Surface Area 1/2*pi*Radius at curve centroid)
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