Volume Of Solid Of Revolution Given Surface To Volume Ratio Calculator

Formula Used:

\[ V = (2 \pi r_{Area\ Centroid}) \times \frac{LSA + ((r_{Top} + r_{Bottom})^2 \pi)}{2 \pi r_{Area\ Centroid} (RA/V)} \]

Radius at Area Centroid of Solid of Revolution:

Lateral Surface Area of Solid of Revolution:

m²

Top Radius of Solid of Revolution:

Bottom Radius of Solid of Revolution:

Surface to Volume Ratio of Solid of Revolution:

1/m

Volume of Solid of Revolution:

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1. What is the Volume of Solid of Revolution?

The Volume of Solid of Revolution is the total quantity of three dimensional space enclosed by the entire surface of the Solid of Revolution. It represents the space occupied by a 3D object created by rotating a 2D curve around an axis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = (2 \pi r_{Area\ Centroid}) \times \frac{LSA + ((r_{Top} + r_{Bottom})^2 \pi)}{2 \pi r_{Area\ Centroid} (RA/V)} \]

Where:

\( V \) — Volume of Solid of Revolution (m³)
\( r_{Area\ Centroid} \) — Radius at Area Centroid of Solid of Revolution (m)
\( LSA \) — Lateral Surface Area of Solid of Revolution (m²)
\( r_{Top} \) — Top Radius of Solid of Revolution (m)
\( r_{Bottom} \) — Bottom Radius of Solid of Revolution (m)
\( RA/V \) — Surface to Volume Ratio of Solid of Revolution (1/m)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the volume of a solid generated by revolving a plane area about an axis, incorporating geometric properties and surface-to-volume ratio.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining material requirements, structural analysis, fluid capacity, and various engineering applications involving rotational solids.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive (except radii which can be zero). Use consistent units throughout the calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Solid of Revolution?
A: A Solid of Revolution is a three-dimensional object obtained by rotating a two-dimensional curve around an axis.

Q2: What is the Area Centroid?
A: The Area Centroid is the geometric center of the area being revolved, representing the average position of all points in the area.

Q3: How is Surface to Volume Ratio defined?
A: Surface to Volume Ratio is the ratio of the surface area of a solid to its volume, indicating how much surface area is available per unit volume.

Q4: What are typical applications of this calculation?
A: This calculation is used in mechanical engineering, architecture, manufacturing, and physics for designing rotational components, containers, and structural elements.

Q5: Are there limitations to this formula?
A: This formula assumes specific geometric properties and may have limitations for complex shapes or irregular solids of revolution.