Lateral Surface Area of Paraboloid given Surface to Volume Ratio 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]			+10% -10%

✖Lateral Surface Area of Paraboloid is the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid.ⓘ Lateral Surface Area of Paraboloid given Surface to Volume Ratio [LSA]

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Formula

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Lateral Surface Area of Paraboloid given Surface to Volume Ratio

Formula

`"LSA" = 1/2*pi*"r"^2*"h"*"R"_{"A/V"}-pi*"r"^2`

Example

`"1099.557m²"=1/2*pi*("5m")^2*"50m"*"0.6m⁻¹"-pi*("5m")^2`

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Lateral Surface Area of Paraboloid given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Lateral Surface Area of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid*Surface to Volume Ratio of Paraboloid-pi*Radius of Paraboloid^2
LSA = 1/2*pi*r^2*h*R_A/V-pi*r^2
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Lateral Surface Area of Paraboloid - (Measured in Square Meter) - Lateral Surface Area of Paraboloid is the total quantity of two dimensional plane enclosed on the lateral curved surface of 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.
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.

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
Surface to Volume Ratio of Paraboloid: 0.6 1 per Meter --> 0.6 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

LSA = 1/2*pi*r^2*h*R_A/V-pi*r^2 --> 1/2*pi*5^2*50*0.6-pi*5^2

Evaluating ... ...

LSA = 1099.55742875643

STEP 3: Convert Result to Output's Unit

1099.55742875643 Square Meter --> No Conversion Required

FINAL ANSWER

1099.55742875643 ≈ 1099.557 Square Meter <-- Lateral Surface Area of Paraboloid

(Calculation completed in 00.035 seconds)

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Home » Math » Geometry » 3D Geometry » Paraboloid » Surface Area of Paraboloid » Lateral Surface Area of Paraboloid » Lateral Surface Area of Paraboloid given Surface to Volume Ratio

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Created by Divanshi Jain

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

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< 6 Lateral Surface Area of Paraboloid Calculators

Lateral Surface Area of Paraboloid given Volume

Go Lateral Surface Area of Paraboloid = (pi*sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid)))/(6*Height of Paraboloid^2)*(((2*Volume of Paraboloid)/(pi*Height of Paraboloid)+4*Height of Paraboloid^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2))

Lateral Surface Area of Paraboloid

Go Lateral Surface Area 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)

Lateral Surface Area of Paraboloid given Surface to Volume Ratio

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

Lateral Surface Area of Paraboloid given Radius

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

Lateral Surface Area of Paraboloid given Height

Go Lateral Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Height of Paraboloid*Shape Parameter of Paraboloid)^(3/2)-1)

Lateral Surface Area of Paraboloid given Total Surface Area

Go Lateral Surface Area of Paraboloid = Total Surface Area of Paraboloid-pi*Radius of Paraboloid^2

Lateral Surface Area of Paraboloid given Surface to Volume Ratio Formula

Lateral Surface Area of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid*Surface to Volume Ratio of Paraboloid-pi*Radius of Paraboloid^2
LSA = 1/2*pi*r^2*h*R_A/V-pi*r^2

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 Lateral Surface Area of Paraboloid given Surface to Volume Ratio?

Lateral Surface Area of Paraboloid given Surface to Volume Ratio calculator uses Lateral Surface Area of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid*Surface to Volume Ratio of Paraboloid-pi*Radius of Paraboloid^2 to calculate the Lateral Surface Area of Paraboloid, The Lateral Surface Area of Paraboloid given Surface to Volume Ratio formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid, calculated using surface to volume ratio of Paraboloid. Lateral Surface Area of Paraboloid is denoted by LSA symbol.

How to calculate Lateral Surface Area of Paraboloid given Surface to Volume Ratio using this online calculator? To use this online calculator for Lateral Surface Area of Paraboloid given Surface to Volume Ratio, enter Radius of Paraboloid (r), Height of Paraboloid (h) & Surface to Volume Ratio of Paraboloid (R_A/V) and hit the calculate button. Here is how the Lateral Surface Area of Paraboloid given Surface to Volume Ratio calculation can be explained with given input values -> 1099.557 = 1/2*pi*5^2*50*0.6-pi*5^2.

FAQ

What is Lateral Surface Area of Paraboloid given Surface to Volume Ratio?

The Lateral Surface Area of Paraboloid given Surface to Volume Ratio formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid, calculated using surface to volume ratio of Paraboloid and is represented as LSA = 1/2*pi*r^2*h*R_A/V-pi*r^2 or Lateral Surface Area of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid*Surface to Volume Ratio of Paraboloid-pi*Radius of Paraboloid^2. 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 & Surface to Volume Ratio of Paraboloid is the numerical ratio of the total surface area of the Paraboloid to the volume of the Paraboloid.

How to calculate Lateral Surface Area of Paraboloid given Surface to Volume Ratio?

The Lateral Surface Area of Paraboloid given Surface to Volume Ratio formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid, calculated using surface to volume ratio of Paraboloid is calculated using Lateral Surface Area of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid*Surface to Volume Ratio of Paraboloid-pi*Radius of Paraboloid^2. To calculate Lateral Surface Area of Paraboloid given Surface to Volume Ratio, you need Radius of Paraboloid (r), Height of Paraboloid (h) & Surface to Volume Ratio of Paraboloid (R_A/V). With our tool, you need to enter the respective value for Radius of Paraboloid, Height of Paraboloid & Surface to Volume Ratio 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 Lateral Surface Area of Paraboloid?

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

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

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