Volume of Solid of Revolution given Lateral Surface Area Calculator

✖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 Solid of Revolution [A_Curve]			+10% -10%
✖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%
✖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%

✖Volume of Solid of Revolution is the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution.ⓘ Volume of Solid of Revolution given Lateral Surface Area [V]

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Volume of Solid of Revolution given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Solid of Revolution - (Measured in Cubic Meter) - Volume of Solid of Revolution is the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution.
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.
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

Area under Curve Solid of Revolution: 50 Square Meter --> 50 Square Meter No Conversion Required
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
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

V = (2*pi*A_Curve)*((LSA+(((r_Top+r_Bottom)^2)*pi))/(2*pi*A_Curve*R_A/V)) --> (2*pi*50)*((2360+(((10+20)^2)*pi))/(2*pi*50*1.3))

Evaluating ... ...

V = 3990.33337556216

STEP 3: Convert Result to Output's Unit

3990.33337556216 Cubic Meter --> No Conversion Required

FINAL ANSWER

3990.33337556216 ≈ 3990.333 Cubic Meter <-- Volume of Solid of Revolution

(Calculation completed in 00.008 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< Volume of Solid of Revolution Calculators

Volume of Solid of Revolution given Surface to Volume Ratio

LaTeX Go 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))

Volume of Solid of Revolution given Lateral Surface Area

LaTeX Go 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))

Volume of Solid of Revolution

LaTeX Go 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 given Lateral Surface Area Formula

LaTeX Go

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 Volume of Solid of Revolution given Lateral Surface Area?

Volume of Solid of Revolution given Lateral Surface Area calculator uses 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)) to calculate the Volume of Solid of Revolution, Volume of Solid of Revolution given Lateral Surface Area formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution, calculated using its lateral surface area. Volume of Solid of Revolution is denoted by V symbol.

How to calculate Volume of Solid of Revolution given Lateral Surface Area using this online calculator? To use this online calculator for Volume of Solid of Revolution given Lateral Surface Area, enter Area under Curve Solid of Revolution (A_Curve), 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. Here is how the Volume of Solid of Revolution given Lateral Surface Area calculation can be explained with given input values -> 3990.333 = (2*pi*50)*((2360+(((10+20)^2)*pi))/(2*pi*50*1.3)).

FAQ

What is Volume of Solid of Revolution given Lateral Surface Area?

Volume of Solid of Revolution given Lateral Surface Area formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution, calculated using its lateral surface area and is represented as V = (2*pi*A_Curve)*((LSA+(((r_Top+r_Bottom)^2)*pi))/(2*pi*A_Curve*R_A/V)) or 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)). 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 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 & 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 Volume of Solid of Revolution given Lateral Surface Area?

Volume of Solid of Revolution given Lateral Surface Area formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution, calculated using its lateral surface area is calculated using 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)). To calculate Volume of Solid of Revolution given Lateral Surface Area, you need Area under Curve Solid of Revolution (A_Curve), 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). With our tool, you need to enter the respective value for 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 & 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 Volume of Solid of Revolution?

In this formula, Volume of Solid of Revolution 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 & Surface to Volume Ratio of Solid of Revolution. We can use 2 other way(s) to calculate the same, which is/are as follows -

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*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))

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