Surface to Volume Ratio of Paraboloid Calculator

✖Radius of Paraboloid is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid.ⓘ Radius of Paraboloid [r]			+10% -10%
✖Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.ⓘ Height of Paraboloid [h]			+10% -10%

✖Surface to Volume Ratio of Paraboloid is the numerical ratio of the total surface area of the Paraboloid to the volume of the Paraboloid.ⓘ Surface to Volume Ratio of Paraboloid [R_A/V]

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Formula

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Surface to Volume Ratio of Paraboloid

Formula

`"R"_{"A/V"} = ((pi*"r")/(6*"h"^2)*(("r"^2+(4*"h"^2))^(3/2)-"r"^3)+(pi*"r"^2))/(1/2*pi*"r"^2*"h")`

Example

`"0.575268m⁻¹"=((pi*"5m")/(6*("50m")^2)*((("5m")^2+(4*("50m")^2))^(3/2)-("5m")^3)+(pi*("5m")^2))/(1/2*pi*("5m")^2*"50m")`

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Surface to Volume Ratio of Paraboloid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Paraboloid = ((pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+(4*Height of Paraboloid^2))^(3/2)-Radius of Paraboloid^3)+(pi*Radius of Paraboloid^2))/(1/2*pi*Radius of Paraboloid^2*Height of Paraboloid)
R_A/V = ((pi*r)/(6*h^2)*((r^2+(4*h^2))^(3/2)-r^3)+(pi*r^2))/(1/2*pi*r^2*h)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Surface to Volume Ratio of Paraboloid - (Measured in 1 per Meter) - Surface to Volume Ratio of Paraboloid is the numerical ratio of the total surface area of the Paraboloid to the volume of the Paraboloid.
Radius of Paraboloid - (Measured in Meter) - Radius of Paraboloid is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid.
Height of Paraboloid - (Measured in Meter) - Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.

STEP 1: Convert Input(s) to Base Unit

Radius of Paraboloid: 5 Meter --> 5 Meter No Conversion Required
Height of Paraboloid: 50 Meter --> 50 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = ((pi*r)/(6*h^2)*((r^2+(4*h^2))^(3/2)-r^3)+(pi*r^2))/(1/2*pi*r^2*h) --> ((pi*5)/(6*50^2)*((5^2+(4*50^2))^(3/2)-5^3)+(pi*5^2))/(1/2*pi*5^2*50)

Evaluating ... ...

R_A/V = 0.575267916146321

STEP 3: Convert Result to Output's Unit

0.575267916146321 1 per Meter --> No Conversion Required

FINAL ANSWER

0.575267916146321 ≈ 0.575268 1 per Meter <-- Surface to Volume Ratio of Paraboloid

(Calculation completed in 00.004 seconds)

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 6 Surface to Volume Ratio of Paraboloid Calculators

Surface to Volume Ratio of Paraboloid

Go Surface to Volume Ratio of Paraboloid = ((pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+(4*Height of Paraboloid^2))^(3/2)-Radius of Paraboloid^3)+(pi*Radius of Paraboloid^2))/(1/2*pi*Radius of Paraboloid^2*Height of Paraboloid)

Surface to Volume Ratio of Paraboloid given Radius

Go Surface to Volume Ratio of Paraboloid = ((pi/(6*Shape Parameter of Paraboloid^2)*((1+(4*Shape Parameter of Paraboloid^2*Radius of Paraboloid^2))^(3/2)-1))+pi*Radius of Paraboloid^2)/(1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4)

Surface to Volume Ratio of Paraboloid given Volume

Go Surface to Volume Ratio of Paraboloid = (((pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+4*Height of Paraboloid^2)^(3/2)-Radius of Paraboloid^3))+(pi*Radius of Paraboloid^2))/(Volume of Paraboloid)

Surface to Volume Ratio of Paraboloid given Height

Go Surface to Volume Ratio of Paraboloid = (1/(6*Shape Parameter of Paraboloid)*((1+(4*Shape Parameter of Paraboloid*Height of Paraboloid))^(3/2)-1)+Height of Paraboloid)/(1/2*Height of Paraboloid^2)

Surface to Volume Ratio of Paraboloid given Lateral Surface Area

Go Surface to Volume Ratio of Paraboloid = (Lateral Surface Area of Paraboloid+pi*Radius of Paraboloid^2)/(1/2*pi*Radius of Paraboloid^2*Height of Paraboloid)

Surface to Volume Ratio of Paraboloid given Total Surface Area

Go Surface to Volume Ratio of Paraboloid = (2*Total Surface Area of Paraboloid)/(pi*Radius of Paraboloid^2*Height of Paraboloid)

Surface to Volume Ratio of Paraboloid Formula

What is Paraboloid?

In geometry, a Paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane section of a paraboloid by a plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines (in the case of a section by a tangent plane). The paraboloid is elliptic if every other nonempty plane section is either an ellipse, or a single point (in the case of a section by a tangent plane). A paraboloid is either elliptic or hyperbolic.

How to Calculate Surface to Volume Ratio of Paraboloid?

Surface to Volume Ratio of Paraboloid calculator uses Surface to Volume Ratio of Paraboloid = ((pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+(4*Height of Paraboloid^2))^(3/2)-Radius of Paraboloid^3)+(pi*Radius of Paraboloid^2))/(1/2*pi*Radius of Paraboloid^2*Height of Paraboloid) to calculate the Surface to Volume Ratio of Paraboloid, The Surface to Volume Ratio of Paraboloid formula is defined as the numerical ratio of the total surface area of the Paraboloid to the volume of the Paraboloid. Surface to Volume Ratio of Paraboloid is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Paraboloid using this online calculator? To use this online calculator for Surface to Volume Ratio of Paraboloid, enter Radius of Paraboloid (r) & Height of Paraboloid (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Paraboloid calculation can be explained with given input values -> 0.575268 = ((pi*5)/(6*50^2)*((5^2+(4*50^2))^(3/2)-5^3)+(pi*5^2))/(1/2*pi*5^2*50).

FAQ

What is Surface to Volume Ratio of Paraboloid?

The Surface to Volume Ratio of Paraboloid formula is defined as the numerical ratio of the total surface area of the Paraboloid to the volume of the Paraboloid and is represented as R_A/V = ((pi*r)/(6*h^2)*((r^2+(4*h^2))^(3/2)-r^3)+(pi*r^2))/(1/2*pi*r^2*h) or Surface to Volume Ratio of Paraboloid = ((pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+(4*Height of Paraboloid^2))^(3/2)-Radius of Paraboloid^3)+(pi*Radius of Paraboloid^2))/(1/2*pi*Radius of Paraboloid^2*Height of Paraboloid). Radius of Paraboloid is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid & Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.

How to calculate Surface to Volume Ratio of Paraboloid?

The Surface to Volume Ratio of Paraboloid formula is defined as the numerical ratio of the total surface area of the Paraboloid to the volume of the Paraboloid is calculated using Surface to Volume Ratio of Paraboloid = ((pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+(4*Height of Paraboloid^2))^(3/2)-Radius of Paraboloid^3)+(pi*Radius of Paraboloid^2))/(1/2*pi*Radius of Paraboloid^2*Height of Paraboloid). To calculate Surface to Volume Ratio of Paraboloid, you need Radius of Paraboloid (r) & Height of Paraboloid (h). With our tool, you need to enter the respective value for Radius of Paraboloid & Height of Paraboloid 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 Surface to Volume Ratio of Paraboloid?

In this formula, Surface to Volume Ratio of Paraboloid uses Radius of Paraboloid & Height of Paraboloid. We can use 5 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Paraboloid = (((pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+4*Height of Paraboloid^2)^(3/2)-Radius of Paraboloid^3))+(pi*Radius of Paraboloid^2))/(Volume of Paraboloid)
Surface to Volume Ratio of Paraboloid = (2*Total Surface Area of Paraboloid)/(pi*Radius of Paraboloid^2*Height of Paraboloid)
Surface to Volume Ratio of Paraboloid = (Lateral Surface Area of Paraboloid+pi*Radius of Paraboloid^2)/(1/2*pi*Radius of Paraboloid^2*Height of Paraboloid)
Surface to Volume Ratio of Paraboloid = ((pi/(6*Shape Parameter of Paraboloid^2)*((1+(4*Shape Parameter of Paraboloid^2*Radius of Paraboloid^2))^(3/2)-1))+pi*Radius of Paraboloid^2)/(1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4)
Surface to Volume Ratio of Paraboloid = (1/(6*Shape Parameter of Paraboloid)*((1+(4*Shape Parameter of Paraboloid*Height of Paraboloid))^(3/2)-1)+Height of Paraboloid)/(1/2*Height of Paraboloid^2)

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