Area under Curve of Solid of Revolution Calculator

✖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.ⓘ Lateral Surface Area of Solid of Revolution [LSA]			+10% -10%
✖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.ⓘ Top Radius of Solid of Revolution [r_Top]			+10% -10%
✖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.ⓘ Bottom Radius of Solid of Revolution [r_Bottom]			+10% -10%
✖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.ⓘ Radius at Area Centroid of Solid of Revolution [r_{Area Centroid}]			+10% -10%
✖Surface to Volume Ratio of Solid of Revolution is defined as the fraction of surface area to volume of Solid of Revolution.ⓘ Surface to Volume Ratio of Solid of Revolution [R_A/V]			+10% -10%

✖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.ⓘ Area under Curve of Solid of Revolution [A_Curve]

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Formula

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Area under Curve of Solid of Revolution

Formula

`"A"_{"Curve"} = ("LSA"+((("r"_{"Top"}+"r"_{"Bottom"})^2)*pi))/(2*pi*"r"_{"Area Centroid"}*"R"_{"A/V"})`

Example

`"52.92344m²"=("2360m²"+((("10m"+"20m")^2)*pi))/(2*pi*"12m"*"1.3m⁻¹")`

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Area under Curve of Solid of Revolution Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
A_Curve = (LSA+(((r_Top+r_Bottom)^2)*pi))/(2*pi*r_{Area Centroid}*R_A/V)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Area under Curve Solid of Revolution - (Measured in Square Meter) - 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.
Lateral Surface Area of Solid of Revolution - (Measured in Square Meter) - 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.
Top Radius of Solid of Revolution - (Measured in Meter) - 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.
Bottom Radius of Solid of Revolution - (Measured in Meter) - 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.
Radius at Area Centroid of Solid of Revolution - (Measured in Meter) - 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.
Surface to Volume Ratio of Solid of Revolution - (Measured in 1 per Meter) - Surface to Volume Ratio of Solid of Revolution is defined as the fraction of surface area to volume of Solid of Revolution.

STEP 1: Convert Input(s) to Base Unit

Lateral Surface Area of Solid of Revolution: 2360 Square Meter --> 2360 Square Meter No Conversion Required
Top Radius of Solid of Revolution: 10 Meter --> 10 Meter No Conversion Required
Bottom Radius of Solid of Revolution: 20 Meter --> 20 Meter No Conversion Required
Radius at Area Centroid of Solid of Revolution: 12 Meter --> 12 Meter No Conversion Required
Surface to Volume Ratio of Solid of Revolution: 1.3 1 per Meter --> 1.3 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Curve = (LSA+(((r_Top+r_Bottom)^2)*pi))/(2*pi*r_{Area Centroid}*R_A/V) --> (2360+(((10+20)^2)*pi))/(2*pi*12*1.3)

Evaluating ... ...

A_Curve = 52.9234401087739

STEP 3: Convert Result to Output's Unit

52.9234401087739 Square Meter --> No Conversion Required

FINAL ANSWER

52.9234401087739 ≈ 52.92344 Square Meter <-- Area under Curve Solid of Revolution

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Solid of Revolution » Area under Curve of Solid of Revolution » Area under Curve of Solid of Revolution

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< 2 Area under Curve of Solid of Revolution Calculators

Area under Curve of Solid of Revolution

Go 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)

Area under Curve of Solid of Revolution given Volume

Go Area under Curve Solid of Revolution = Volume of Solid of Revolution/(2*pi*Radius at Area Centroid of Solid of Revolution)

Area under Curve of Solid of Revolution Formula

What is Solid of Revolution?

A Solid of Revolution is a solid figure obtained by rotating a plane figure around some straight line that lies on the same plane. The surface created by this revolution and which bounds the solid is the surface of revolution.

How to Calculate Area under Curve of Solid of Revolution?

Area under Curve of Solid of Revolution calculator 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 calculate 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 A_Curve 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 of Solid of Revolution (LSA), Top Radius of Solid of Revolution (r_Top), Bottom Radius of Solid of Revolution (r_Bottom), Radius at Area Centroid of Solid of Revolution (r_{Area Centroid}) & Surface to Volume Ratio of Solid of Revolution (R_A/V) and hit the calculate button. Here is how the Area under Curve of Solid of Revolution calculation can be explained with given input values -> 52.92344 = (2360+(((10+20)^2)*pi))/(2*pi*12*1.3).

FAQ

What is Area under Curve of 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 and is represented as A_Curve = (LSA+(((r_Top+r_Bottom)^2)*pi))/(2*pi*r_{Area Centroid}*R_A/V) or 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). 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, 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, 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, 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 & Surface to Volume Ratio of Solid of Revolution is defined as the fraction of surface area to volume of Solid of Revolution.

How to calculate Area under Curve of 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 is calculated using 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 calculate Area under Curve of Solid of Revolution, you need Lateral Surface Area of Solid of Revolution (LSA), Top Radius of Solid of Revolution (r_Top), Bottom Radius of Solid of Revolution (r_Bottom), Radius at Area Centroid of Solid of Revolution (r_{Area Centroid}) & Surface to Volume Ratio of Solid of Revolution (R_A/V). With our tool, you need to enter the respective value for Lateral Surface Area of Solid of Revolution, Top Radius of Solid of Revolution, Bottom Radius of Solid of Revolution, Radius at Area Centroid of Solid of Revolution & Surface to Volume Ratio of Solid of Revolution 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 Solid of Revolution?

In this formula, Area under Curve Solid of Revolution uses Lateral Surface Area of Solid of Revolution, Top Radius of Solid of Revolution, Bottom Radius of Solid of Revolution, Radius at Area Centroid of Solid of Revolution & Surface to Volume Ratio of Solid of Revolution. We can use 1 other way(s) to calculate the same, which is/are as follows -

Area under Curve Solid of Revolution = Volume of Solid of Revolution/(2*pi*Radius at Area Centroid of Solid of Revolution)

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