Volume of Solid of Revolution given Surface to Volume Ratio Calculator

✖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%
✖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 Surface to Volume Ratio [V]

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Volume of Solid of Revolution given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
V = (2*pi*r_{Area Centroid})*((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

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.
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.
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

Radius at Area Centroid of Solid of Revolution: 12 Meter --> 12 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*r_{Area Centroid})*((LSA+(((r_Top+r_Bottom)^2)*pi))/(2*pi*r_{Area Centroid}*R_A/V)) --> (2*pi*12)*((2360+(((10+20)^2)*pi))/(2*pi*12*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 00.007 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 Surface to Volume Ratio 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 Surface to Volume Ratio?

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

How to calculate Volume of Solid of Revolution given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Solid of Revolution given Surface to Volume Ratio, enter Radius at Area Centroid of Solid of Revolution (r_{Area Centroid}), 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 Surface to Volume Ratio calculation can be explained with given input values -> 3990.333 = (2*pi*12)*((2360+(((10+20)^2)*pi))/(2*pi*12*1.3)).

FAQ

What is Volume of Solid of Revolution given Surface to Volume Ratio?

Volume of Solid of Revolution given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution , calculated using its surface to volume ratio and is represented as V = (2*pi*r_{Area Centroid})*((LSA+(((r_Top+r_Bottom)^2)*pi))/(2*pi*r_{Area Centroid}*R_A/V)) or 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)). 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, 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 Surface to Volume Ratio?

Volume of Solid of Revolution given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution , calculated using its surface to volume ratio is calculated using 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)). To calculate Volume of Solid of Revolution given Surface to Volume Ratio, you need Radius at Area Centroid of Solid of Revolution (r_{Area Centroid}), 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 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 & 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 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 & 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*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))

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