Volume of Paraboloid given Lateral Surface Area Calculator

✖Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid.ⓘ Shape Parameter of Paraboloid [p]			+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 [LSA]			+10% -10%

✖Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid.ⓘ Volume of Paraboloid given Lateral Surface Area [V]

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Formula

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Volume of Paraboloid given Lateral Surface Area

Formula

`"V" = pi/(32*"p"^3)*(((6*"LSA"*"p"^2)/pi+1)^(2/3)-1)^2`

Example

`"1961.009m³"=pi/(32*("2")^3)*(((6*"1050m²"*("2")^2)/pi+1)^(2/3)-1)^2`

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Volume of Paraboloid given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2
V = pi/(32*p^3)*(((6*LSA*p^2)/pi+1)^(2/3)-1)^2
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Paraboloid - (Measured in Cubic Meter) - Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid.
Shape Parameter of Paraboloid - Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid.
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.

STEP 1: Convert Input(s) to Base Unit

Shape Parameter of Paraboloid: 2 --> No Conversion Required
Lateral Surface Area of Paraboloid: 1050 Square Meter --> 1050 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = pi/(32*p^3)*(((6*LSA*p^2)/pi+1)^(2/3)-1)^2 --> pi/(32*2^3)*(((6*1050*2^2)/pi+1)^(2/3)-1)^2

Evaluating ... ...

V = 1961.00867116747

STEP 3: Convert Result to Output's Unit

1961.00867116747 Cubic Meter --> No Conversion Required

FINAL ANSWER

1961.00867116747 ≈ 1961.009 Cubic Meter <-- Volume of Paraboloid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Paraboloid » Important Formulas of Paraboloid » Volume of Paraboloid » Volume of Paraboloid given Lateral Surface Area

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

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< 4 Volume of Paraboloid Calculators

Volume of Paraboloid given Lateral Surface Area

Go Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2

Volume of Paraboloid given Height

Go Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid

Volume of Paraboloid given Radius

Go Volume of Paraboloid = 1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4

Volume of Paraboloid

Go Volume of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid

Volume of Paraboloid given Lateral Surface Area Formula

Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2
V = pi/(32*p^3)*(((6*LSA*p^2)/pi+1)^(2/3)-1)^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 Volume of Paraboloid given Lateral Surface Area?

Volume of Paraboloid given Lateral Surface Area calculator uses Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2 to calculate the Volume of Paraboloid, The Volume of Paraboloid given Lateral Surface Area formula is defined as amount of three dimensional space occupied by Paraboloid, calculated using lateral surface area of Paraboloid. Volume of Paraboloid is denoted by V symbol.

How to calculate Volume of Paraboloid given Lateral Surface Area using this online calculator? To use this online calculator for Volume of Paraboloid given Lateral Surface Area, enter Shape Parameter of Paraboloid (p) & Lateral Surface Area of Paraboloid (LSA) and hit the calculate button. Here is how the Volume of Paraboloid given Lateral Surface Area calculation can be explained with given input values -> 1961.009 = pi/(32*2^3)*(((6*1050*2^2)/pi+1)^(2/3)-1)^2.

FAQ

What is Volume of Paraboloid given Lateral Surface Area?

The Volume of Paraboloid given Lateral Surface Area formula is defined as amount of three dimensional space occupied by Paraboloid, calculated using lateral surface area of Paraboloid and is represented as V = pi/(32*p^3)*(((6*LSA*p^2)/pi+1)^(2/3)-1)^2 or Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2. Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid & Lateral Surface Area of Paraboloid is the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid.

How to calculate Volume of Paraboloid given Lateral Surface Area?

The Volume of Paraboloid given Lateral Surface Area formula is defined as amount of three dimensional space occupied by Paraboloid, calculated using lateral surface area of Paraboloid is calculated using Volume of Paraboloid = pi/(32*Shape Parameter of Paraboloid^3)*(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)^2. To calculate Volume of Paraboloid given Lateral Surface Area, you need Shape Parameter of Paraboloid (p) & Lateral Surface Area of Paraboloid (LSA). With our tool, you need to enter the respective value for Shape Parameter of Paraboloid & Lateral Surface Area 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 Volume of Paraboloid?

In this formula, Volume of Paraboloid uses Shape Parameter of Paraboloid & Lateral Surface Area of Paraboloid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid
Volume of Paraboloid = 1/2*(pi*Height of Paraboloid^2)/Shape Parameter of Paraboloid
Volume of Paraboloid = 1/2*pi*Shape Parameter of Paraboloid*Radius of Paraboloid^4

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