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Walchand College of Engineering (WCE), Sangli
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Area under curve of Solid of Revolution given volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
area_under_curve = Volume Polyhedron/(2*pi*Radius at area centroid)
ACurve = Vpolyhedron/(2*pi*rAreaCentroid)
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Volume Polyhedron - Volume Polyhedron is amount of three dimensional space covered by polyhedron. (Measured in Cubic Meter)
Radius at area centroid - Radius at area centroid is the radius measured at area centroid. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Volume Polyhedron: 1200 Cubic Meter --> 1200 Cubic Meter No Conversion Required
Radius at area centroid: 5 Meter --> 5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ACurve = Vpolyhedron/(2*pi*rAreaCentroid) --> 1200/(2*pi*5)
Evaluating ... ...
ACurve = 38.1971863420549
STEP 3: Convert Result to Output's Unit
38.1971863420549 Square Meter --> No Conversion Required
FINAL ANSWER
38.1971863420549 Square Meter <-- Area under curve
(Calculation completed in 00.015 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 given volume Formula

area_under_curve = Volume Polyhedron/(2*pi*Radius at area centroid)
ACurve = Vpolyhedron/(2*pi*rAreaCentroid)

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 given volume?

Area under curve of Solid of Revolution given volume calculator uses area_under_curve = Volume Polyhedron/(2*pi*Radius at area centroid) to calculate the Area under curve, The Area under curve of Solid of Revolution given Volume 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 given volume using this online calculator? To use this online calculator for Area under curve of Solid of Revolution given volume, enter Volume Polyhedron (Vpolyhedron) & Radius at area centroid (rAreaCentroid) and hit the calculate button. Here is how the Area under curve of Solid of Revolution given volume calculation can be explained with given input values -> 38.19719 = 1200/(2*pi*5).

FAQ

What is Area under curve of Solid of Revolution given volume?
The Area under curve of Solid of Revolution given Volume formula is defined as definite integral of a curve and is represented as ACurve = Vpolyhedron/(2*pi*rAreaCentroid) or area_under_curve = Volume Polyhedron/(2*pi*Radius at area centroid). Volume Polyhedron is amount of three dimensional space covered by polyhedron & Radius at area centroid is the radius measured at area centroid.
How to calculate Area under curve of Solid of Revolution given volume?
The Area under curve of Solid of Revolution given Volume formula is defined as definite integral of a curve is calculated using area_under_curve = Volume Polyhedron/(2*pi*Radius at area centroid). To calculate Area under curve of Solid of Revolution given volume, you need Volume Polyhedron (Vpolyhedron) & Radius at area centroid (rAreaCentroid). With our tool, you need to enter the respective value for Volume Polyhedron & Radius at area centroid 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 Volume Polyhedron & Radius at area centroid. 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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