Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio Formula

GoRadius at Area Centroid of Solid of Revolution Formula

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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. Check FAQs

r Area Centroid = \frac{LSA + (({(r Top + r Bottom)}^{2}) \cdot π)}{2 \cdot π \cdot A Curve \cdot R A/V}

r_{Area Centroid} - Radius at Area Centroid of Solid of Revolution?LSA - Lateral Surface Area of Solid of Revolution?r_Top - Top Radius of Solid of Revolution?r_Bottom - Bottom Radius of Solid of Revolution?A_Curve - Area under Curve Solid of Revolution?R_A/V - Surface to Volume Ratio of Solid of Revolution?π - Archimedes' constant?

Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio Example

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Here is how the Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio equation looks like with Values.

Here is how the Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio equation looks like with Units.

Here is how the Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio equation looks like.

12.7016 = \frac{2360 + (({(10 + 20)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 50 \cdot 1.3}

12.7016m = \frac{2360m² + (({(10m + 20m)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 50m² \cdot 1.3m⁻¹}

12.7016 = \frac{2360 + (({(10 + 20)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 50 \cdot 1.3}

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Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio Solution

Follow our step by step solution on how to calculate Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio?

FIRST Step Consider the formula

r Area Centroid = \frac{LSA + (({(r Top + r Bottom)}^{2}) \cdot π)}{2 \cdot π \cdot A Curve \cdot R A/V}

Next Step Substitute values of Variables

∴

r Area Centroid = \frac{2360m² + (({(10m + 20m)}^{2}) \cdot π)}{2 \cdot π \cdot 50m² \cdot 1.3m⁻¹}

Next Step Substitute values of Constants

∴

r Area Centroid = \frac{2360m² + (({(10m + 20m)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 50m² \cdot 1.3m⁻¹}

Next Step Prepare to Evaluate

∴

r Area Centroid = \frac{2360 + (({(10 + 20)}^{2}) \cdot 3.1416)}{2 \cdot 3.1416 \cdot 50 \cdot 1.3}

Next Step Evaluate

∴

r Area Centroid = 12.7016256261057m

LAST Step Rounding Answer

∴

r Area Centroid = 12.7016m

Radius at Area Centroid of Solid of Revolution given Surface to Volume Ratio Formula Elements

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Radius at Area Centroid 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.

Symbol: r_{Area Centroid}

Measurement: LengthUnit: m